期刊：
Expert Systems with Applications,2026年299:129968 ISSN：0957-4174
通讯作者：
Zhifeng Dai
作者机构：
[Huali Huang; Qinnan Jiang] College of Mathematics and Statistics, Changsha University of Science and Technology, Hunan, China;Beijing Huairou Laboratory, Bejing, 101499, Peoples R China;[Yaling Chen] School of Humanity and Management, Hunan University of Chinese Medicine, Changsha, Hunan, China;State Key Laboratory of Disaster Prevention & Reduction for Power Grid, Changsha University of Science & Technology, Changsha 410114, China;[Zhifeng Dai] College of Mathematics and Statistics, Changsha University of Science and Technology, Hunan, China<&wdkj&>Beijing Huairou Laboratory, Bejing, 101499, Peoples R China<&wdkj&>State Key Laboratory of Disaster Prevention & Reduction for Power Grid, Changsha University of Science & Technology, Changsha 410114, China
通讯机构：
[Zhifeng Dai] C;College of Mathematics and Statistics, Changsha University of Science and Technology, Hunan, China<&wdkj&>Beijing Huairou Laboratory, Bejing, 101499, Peoples R China<&wdkj&>State Key Laboratory of Disaster Prevention & Reduction for Power Grid, Changsha University of Science & Technology, Changsha 410114, China
摘要：
In order to better apply the advantages of deep learning models in crude oil price prediction, this paper proposes a novel deep learning combined model. It has a “decomposition and construction, dual-model parallel feature and extraction fully connected fusion” architecture, which combines the Transformer model with self-attention mechanism, the convolutional neural network (CNN) with local feature extraction in “parallel” and a fully connected neural network (FCN) to realize feature fusion. Firstly, the original price sequence is decomposed into multiple intrinsic mode functions through variational mode decomposition (VMD), and then the component with the highest Lempel-Ziv complexity (LZC) is processed by the empirical mode decomposition (EMD). Furthermore, model each component obtained from two decomposition using the Transformer-CNN model separately to obtain their predicted values. Finally, the final prediction results are derived from a linear combination of the predicted values of all components. Empirical analysis has demonstrated that the proposed model has better performance than benchmark models, and a series of tests have demonstrated its robustness. In conclusion, it represents a collaborative mechanism of decomposition as the foundation, dual models performing their respective duties, and fusion amplifying advantages. The application of this model in this paper significantly improves the forecasting accuracy of crude oil prices, which is helpful for investors and managers to grasp the trend of oil price changes and make response strategies.
In order to better apply the advantages of deep learning models in crude oil price prediction, this paper proposes a novel deep learning combined model. It has a “decomposition and construction, dual-model parallel feature and extraction fully connected fusion” architecture, which combines the Transformer model with self-attention mechanism, the convolutional neural network (CNN) with local feature extraction in “parallel” and a fully connected neural network (FCN) to realize feature fusion. Firstly, the original price sequence is decomposed into multiple intrinsic mode functions through variational mode decomposition (VMD), and then the component with the highest Lempel-Ziv complexity (LZC) is processed by the empirical mode decomposition (EMD). Furthermore, model each component obtained from two decomposition using the Transformer-CNN model separately to obtain their predicted values. Finally, the final prediction results are derived from a linear combination of the predicted values of all components. Empirical analysis has demonstrated that the proposed model has better performance than benchmark models, and a series of tests have demonstrated its robustness. In conclusion, it represents a collaborative mechanism of decomposition as the foundation, dual models performing their respective duties, and fusion amplifying advantages. The application of this model in this paper significantly improves the forecasting accuracy of crude oil prices, which is helpful for investors and managers to grasp the trend of oil price changes and make response strategies.
期刊：
Journal of Mathematical Analysis and Applications,2026年552(2):129825 ISSN：0022-247X
通讯作者：
Liu, SL
作者机构：
[Li, Yongsheng; Liang, Tao] South China Univ Technol, Sch Math, Guangzhou 510640, Peoples R China.;[Liu, SL; Liu, Sili] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
通讯机构：
[Liu, SL ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
关键词：
Compressible Oldroyd-B model;Global large solution;Besov space;Littlewood-Paley theory
摘要：
In this paper, we investigate the d -dimensional( d ≥ 2 ) compressible Oldroyd-B model proposed by Barrett, Lu, Süli (Commun. Math. Sci., 15, 1265–1323, 2017). By employing weighted Chemin-Lerner technique and a dedicated energy argument, we establish the global well-posedness of partially large solutions. Our findings indicate that the incompressible part of the stress tensor T can grow arbitrarily large.
In this paper, we investigate the d -dimensional( d ≥ 2 ) compressible Oldroyd-B model proposed by Barrett, Lu, Süli (Commun. Math. Sci., 15, 1265–1323, 2017). By employing weighted Chemin-Lerner technique and a dedicated energy argument, we establish the global well-posedness of partially large solutions. Our findings indicate that the incompressible part of the stress tensor T can grow arbitrarily large.
期刊：
Journal of Mathematical Analysis and Applications,2026年555(1):130048 ISSN：0022-247X
通讯作者：
Kang Zhao
作者机构：
[Kang Zhao; Jiantian Wang; Fangting Deng] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, PR China
通讯机构：
[Kang Zhao] S;School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, PR China
摘要：
In this paper, the partial quadratic eigenvalue assignment problem (PQEAP) for the singular second-order system by the acceleration-velocity-displacement active controller was considered. Based on the spectral decomposition of quadratic symmetric pencil, a sufficient and necessary condition of the closed-loop to preserve no spill-over is provided. Using the receptances and system matrices, the parametric solutions of the PQEAP are characterized. Finally, a gradient-based optimization algorithm for the robust and minimum norm solution of the PQEAP is proposed. Numerical examples show the robustness and effectiveness of the proposed method.
In this paper, the partial quadratic eigenvalue assignment problem (PQEAP) for the singular second-order system by the acceleration-velocity-displacement active controller was considered. Based on the spectral decomposition of quadratic symmetric pencil, a sufficient and necessary condition of the closed-loop to preserve no spill-over is provided. Using the receptances and system matrices, the parametric solutions of the PQEAP are characterized. Finally, a gradient-based optimization algorithm for the robust and minimum norm solution of the PQEAP is proposed. Numerical examples show the robustness and effectiveness of the proposed method.
摘要：
In this paper, we propose a regularized lattice Boltzmann model for one-dimensional nonlinear scalar hyperbolic conservation laws which can convert to convection–diffusion equation through introducing a dissipation term. Then, a rigorous Chapman–Enskog analysis is conducted to show that this models can recover the correct governing equation. Finally, we also conduct some simulations to test the model and find that the numerical results not only agree with the exact solutions but also exhibits superior performance in solving hyperbolic conservation laws with discontinuous initial conditions.
In this paper, we propose a regularized lattice Boltzmann model for one-dimensional nonlinear scalar hyperbolic conservation laws which can convert to convection–diffusion equation through introducing a dissipation term. Then, a rigorous Chapman–Enskog analysis is conducted to show that this models can recover the correct governing equation. Finally, we also conduct some simulations to test the model and find that the numerical results not only agree with the exact solutions but also exhibits superior performance in solving hyperbolic conservation laws with discontinuous initial conditions.
期刊：
Communications in Nonlinear Science and Numerical Simulation,2026年152:109229 ISSN：1007-5704
通讯作者：
Timoshin, SA
作者机构：
[Li, Jing; Zhang, Rongshao] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.;[Li, Jing; Zhang, Rongshao] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha, Peoples R China.;[Timoshin, Sergey A.] Xian Jiaotong Liverpool Univ, Sch Math & Phys, Suzhou, Jiangsu, Peoples R China.
通讯机构：
[Timoshin, SA ] X;Xian Jiaotong Liverpool Univ, Sch Math & Phys, Suzhou, Jiangsu, Peoples R China.
关键词：
Asymptotic almost periodicity;Fixed point theorem for condensing mappings;Multivalued mapping;Mild solution;Resolvent operator;Nonlocal condition;Integro-differential inclusion
摘要：
This paper studies a class of first-order abstract integro-differential inclusions defined on a Banach space. Our system is characterized by time-varying evolution operators and, notably, nonlocal initial conditions formulated as set inclusions. The motivation for this research stems from the need for more accurate modeling of complex physical and biological systems exhibiting memory effects, where traditional local or single-valued nonlocal conditions prove insufficient. Employing techniques from resolvent operator theory, fixed point arguments involving measures of non-compact-ness, and the properties of multivalued mappings, we prove the existence of mild solutions for the proposed integro-differential inclusion problem, avoiding the restrictive assumptions on the compactness of the associated resolvent operators. In addition, we establish conditions for the existence of asymptotically almost periodic solutions, necessary for understanding the long-term behavior of systems subjected to time-varying influences and possessing memory. The interplay between time-dependence, hereditary effects, nonlinear multivalued dynamics, and multivalued nonlocal conditions makes the study of such asymptotic behavior particularly relevant. To illustrate the applicability of our abstract theoretical framework, we conclude the paper with an example.
This paper studies a class of first-order abstract integro-differential inclusions defined on a Banach space. Our system is characterized by time-varying evolution operators and, notably, nonlocal initial conditions formulated as set inclusions. The motivation for this research stems from the need for more accurate modeling of complex physical and biological systems exhibiting memory effects, where traditional local or single-valued nonlocal conditions prove insufficient.
Employing techniques from resolvent operator theory, fixed point arguments involving measures of non-compact-ness, and the properties of multivalued mappings, we prove the existence of mild solutions for the proposed integro-differential inclusion problem, avoiding the restrictive assumptions on the compactness of the associated resolvent operators. In addition, we establish conditions for the existence of asymptotically almost periodic solutions, necessary for understanding the long-term behavior of systems subjected to time-varying influences and possessing memory. The interplay between time-dependence, hereditary effects, nonlinear multivalued dynamics, and multivalued nonlocal conditions makes the study of such asymptotic behavior particularly relevant.
To illustrate the applicability of our abstract theoretical framework, we conclude the paper with an example.
期刊：
International Journal of Approximate Reasoning,2025年186:109516 ISSN：0888-613X
通讯作者：
Guangming Lang
作者机构：
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, PR China;Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, Hunan, 410114, PR China;[Hu, Mengjun] Department of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, B3H 3C3, Canada;[Liu, Jing; Lang, Guangming] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, PR China<&wdkj&>Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, Hunan, 410114, PR China
通讯机构：
[Guangming Lang] S;School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, PR China<&wdkj&>Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, Hunan, 410114, PR China
摘要：
Most existing work on three-way conflict analysis has focused on trisecting agent pairs, agents, or issues. While these trisections lay the groundwork for understanding the nature of conflicts, further actions need to be formulated to address conflict resolution. One of the widely studied approaches is to construct feasible strategies. This paper aims to investigate feasible strategies from two perspectives of consistency and non-consistency. Particularly, we begin with computing the overall rating of a clique of agents based on positive and negative similarity degrees. Afterwards, considering the weights of both agents and issues, we propose weighted consistency and non-consistency measures, which are respectively used to identify the feasible strategies for a clique of agents. Algorithms are developed to identify feasible strategies, L -order feasible strategies, and the corresponding optimal ones. Finally, to demonstrate the practicality, effectiveness, and superiority of the proposed models, we apply them to two commonly used case studies on NBA labor negotiations and development plans for Gansu Province and conduct a sensitivity analysis on parameters and a comparative analysis with existing state-of-the-art conflict analysis approaches. The comparison results demonstrate that our conflict resolution models outperform the conventional approaches by unifying weighted agent-issue evaluation with consistency and non-consistency measures to enable the systematic identification of not only feasible strategies but also optimal solutions.
Most existing work on three-way conflict analysis has focused on trisecting agent pairs, agents, or issues. While these trisections lay the groundwork for understanding the nature of conflicts, further actions need to be formulated to address conflict resolution. One of the widely studied approaches is to construct feasible strategies. This paper aims to investigate feasible strategies from two perspectives of consistency and non-consistency. Particularly, we begin with computing the overall rating of a clique of agents based on positive and negative similarity degrees. Afterwards, considering the weights of both agents and issues, we propose weighted consistency and non-consistency measures, which are respectively used to identify the feasible strategies for a clique of agents. Algorithms are developed to identify feasible strategies, L -order feasible strategies, and the corresponding optimal ones. Finally, to demonstrate the practicality, effectiveness, and superiority of the proposed models, we apply them to two commonly used case studies on NBA labor negotiations and development plans for Gansu Province and conduct a sensitivity analysis on parameters and a comparative analysis with existing state-of-the-art conflict analysis approaches. The comparison results demonstrate that our conflict resolution models outperform the conventional approaches by unifying weighted agent-issue evaluation with consistency and non-consistency measures to enable the systematic identification of not only feasible strategies but also optimal solutions.
摘要：
This paper considers two supercritical branching processes with immigration in different random environments, denoted by $\{Z_{1,n}\}$ and $\{Z_{2,m}\}$, with criticality parameters mu 1 and mu 2, respectively. Under certain conditions, it is known that $\frac{1}{n} \log Z_{1,n} \to \mu_1$ and $\frac{1}{m} \log Z_{2,m} \to \mu_2$ converge in probability as $m, n \to \infty$. We present basic properties about a central limit theorem, a non-uniform Berry-Esseen's bound, and Cram & eacute;r's moderate deviations for $\frac{1}{n} \log Z_{1,n} - \frac{1}{m} \log Z_{2,m}$ as $m, n \to \infty$. To this end, applications to construction of confidence intervals and simulations are also given.
摘要：
This paper investigates the role of time–frequency information in dimension reduction prediction of stock returns . Using the long-term wavelet component of monthly S&P500 excess returns as supervision, we employ a machine learning method to extract the common predictive factor from prevalent macroeconomic variables and construct a new macroeconomic index aligned with stock return prediction. The macroeconomic index exhibits significant predictive power, both in and out of sample, at the market and portfolio levels. It outperforms all individual macroeconomic predictors and the factors based on higher frequency information of realized returns. Our findings demonstrate substantial economic value of the new index in asset allocation. Moreover, we also observe a complementary relation between macroeconomic index and investor sentiment. The predictive power is most pronounced during high-economic-uncertainty periods when investors are likely to underreact to fundamental signals and stems from cash flow predictability channel.
This paper investigates the role of time–frequency information in dimension reduction prediction of stock returns . Using the long-term wavelet component of monthly S&P500 excess returns as supervision, we employ a machine learning method to extract the common predictive factor from prevalent macroeconomic variables and construct a new macroeconomic index aligned with stock return prediction. The macroeconomic index exhibits significant predictive power, both in and out of sample, at the market and portfolio levels. It outperforms all individual macroeconomic predictors and the factors based on higher frequency information of realized returns. Our findings demonstrate substantial economic value of the new index in asset allocation. Moreover, we also observe a complementary relation between macroeconomic index and investor sentiment. The predictive power is most pronounced during high-economic-uncertainty periods when investors are likely to underreact to fundamental signals and stems from cash flow predictability channel.
摘要：
<p style="text-align: justify;">In this paper, a numerical investigation of power-law fluid flow in the trapezoidal cavity has been conducted by incompressible finite-difference lattice Boltzmann
method (IFDLBM). By designing the equilibrium distribution function, the Navier-Stokes equations (NSEs) can be recovered exactly. Through the coordinate transformation method, the body-fitted grid in physical region is transformed into a uniform grid
in computational region. The effect of Reynolds $(Re)$ number, the power-law index $n$ and the vertical angle $θ$ on the trapezoidal cavity are investigated. According to the
numerical results, we come to some conclusions. For low $Re$ number $Re =100,$ it can
be found that the behavior of power-law fluid flow becomes more complicated with
the increase of $n.$ And as vertical angle $θ$ decreases, the flow becomes smooth and the
number of vortices decreases. For high Re numbers, the flow development becomes
more complex, the number and strength of vortices increase. If the Reynolds number
increases further, the power-law fluid will changes from steady flow to periodic flow
and then to turbulent flow. For the steady flow, the lager the $θ,$ the more complicated
the vortices. And the critical Re number from steady to periodic state decreases with
the decrease of power-law index $n.$</p>
摘要：
In this article, we define the notion of n -cotorsion pairs in triangulated categories, which is a generalization of the classical cotorsion pairs. We prove that any mutation of an n -cotorsion pair is again an n -cotorsion pair. When n = 1 , this result generalizes the work of Zhou and Zhu for classical cotorsion pairs. As applications, we give a geometric characterization of n -cotorsion pairs in n -cluster categories of type A and give a geometric realization of mutation of n -cotorsion pairs via rotation of certain configurations of n -diagonals.
In this article, we define the notion of n -cotorsion pairs in triangulated categories, which is a generalization of the classical cotorsion pairs. We prove that any mutation of an n -cotorsion pair is again an n -cotorsion pair. When n = 1 , this result generalizes the work of Zhou and Zhu for classical cotorsion pairs. As applications, we give a geometric characterization of n -cotorsion pairs in n -cluster categories of type A and give a geometric realization of mutation of n -cotorsion pairs via rotation of certain configurations of n -diagonals.
期刊：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES,2025年111(2):e70091- ISSN：0024-6107
通讯作者：
Xu, RZ
作者机构：
[Lin, Qiang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.;[Xu, Runzhang; Lin, Qiang] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China.
通讯机构：
[Xu, RZ ] H;Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China.
摘要：
In this paper, we conduct a comprehensive study of the global well-posedness of solution for a class of nonlocal wave equations with variable-order fractional Laplacian and variable exponent nonlinearity by constructing a suitable framework of the variational theory. We first prove the local-in-time existence of the weak solution via the Galerkin approximation technique and fixed point theory. Then by constructing the potential well theory, we classify the initial data leading to the global existence and finite time blowup of the solution for three different initial energy cases, that is, subcritical initial energy case, critical initial energy case, and supercritical initial energy case. For the subcritical and critical initial energy cases, we show that the solution exists globally in time when the initial data belong to the stable manifold and blows up in finite time when the initial data belong to the unstable manifold. For the supercritical initial energy case, we observe some initial conditions that enable the finite time blow-up solution by an adapted concavity method, and the issue of global existence still remains unsolved. As a further study of finite time blowup, we estimate the upper and lower bounds of blow-up time by using different strategies, that is, applying some first-order differential inequality regardless of the different initial energy levels, to give a unified expression for the lower bound estimation for three initial energy levels. For the upper bound estimation, we utilize two second-order differential inequalities influenced by the different energy levels to give the upper bound estimations of the blow-up time at each initial energy level.
摘要：
This study presents an effective surface reconstruction approach for solving one- and two-dimensional Saint-Venant-Exner models. These models, which couple Saint-Venant equations (hydrodynamics) with the Exner equation (morphodynamics), face significant challenges due to the presence of wet-dry interfaces. We employ the surface reconstruction scheme proposed in [19] to solve the Saint-Venant-Exner system numerically. This work specifically addresses three major difficulties associated with movable bottom topography and wet-dry fronts: (a) precisely preserving stationary solutions; (b) ensuring stability across diverse fluid-sediment coupling regimes, particularly during transitions between intense and weak interactions; and (c) maintaining non-negative water depths at all times. The investigation focuses on how these factors impact system performance under dynamic conditions. The surface reconstruction scheme applied to the Saint-Venant-Exner equations is rigorously proven to preserve positivity during water depth updates. Crucially, it also guarantees the preservation of still-water steady-state solutions. A comprehensive suite of numerical experiments across both one- and two-dimensional Saint-Venant-Exner systems provides compelling evidence. The results confirm that the surface reconstruction method effectively maintains steady-state conditions and non-negative water depths, validating its robustness and reliability.
This study presents an effective surface reconstruction approach for solving one- and two-dimensional Saint-Venant-Exner models. These models, which couple Saint-Venant equations (hydrodynamics) with the Exner equation (morphodynamics), face significant challenges due to the presence of wet-dry interfaces. We employ the surface reconstruction scheme proposed in [19] to solve the Saint-Venant-Exner system numerically. This work specifically addresses three major difficulties associated with movable bottom topography and wet-dry fronts: (a) precisely preserving stationary solutions; (b) ensuring stability across diverse fluid-sediment coupling regimes, particularly during transitions between intense and weak interactions; and (c) maintaining non-negative water depths at all times. The investigation focuses on how these factors impact system performance under dynamic conditions. The surface reconstruction scheme applied to the Saint-Venant-Exner equations is rigorously proven to preserve positivity during water depth updates. Crucially, it also guarantees the preservation of still-water steady-state solutions. A comprehensive suite of numerical experiments across both one- and two-dimensional Saint-Venant-Exner systems provides compelling evidence. The results confirm that the surface reconstruction method effectively maintains steady-state conditions and non-negative water depths, validating its robustness and reliability.
通讯机构：
[Wang, F ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 100190, Peoples R China.
关键词：
Fisher equation;Stream temperature equation;Diffusive SIS model;Global stability
摘要：
In this paper, the global stabilization of solutions to the initial-boundary value problem for the coupled model of the Fisher equation and Stream temperature equation (i.e., Fisher–Stream model) is studied. It is shown that under the non-homogeneous Dirichlet condition, the large time behavior of model analytical solutions is controlled by boundary conditions. Promoting to application, we establish similar conclusions in the coupled equation of the SIS model and Stream temperature equation.
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2025年48(6):1-28 ISSN：0126-6705
通讯作者：
Yingshan Chen
作者机构：
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China;College of Science, National University of Defense Technology, Changsha, China;[Yingshan Chen] School of Mathematics, South China University of Technology, Guangzhou, China;[Sili Liu] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China<&wdkj&>College of Science, National University of Defense Technology, Changsha, China
通讯机构：
[Yingshan Chen] S;School of Mathematics, South China University of Technology, Guangzhou, China
摘要：
This article is devoted to the low Mach number limit of the compressible Oldroyd-B model is rigorously justified in the whole space
$$\mathbb {R}^3$$
. Under some smallness assumptions on the initial data, we first obtain the global wellposedness of strong solution with uniform regularity with respect to the Mach number. Then, the existence of global strong solution to the corresponding incompressible model is proved via the incompressible limits. Moreover, the convergence rates are also obtained associated with
$$L^2$$
-norm in the case of well-prepared initial data.
摘要：
In this paper, the famous Bernfeld–Haddock conjecture is generalized to a broader form combining with a class of non-autonomous delay differential equations. With the help of differential inequality technique and Dini derivative theory, it is proved that each solution of the addressed equations has boundedness and tends to a constant without requiring the delay feedback function to be strictly increasing, which greatly refines and extends the corresponding results in the existing literature. In particular, an explanatory example is performed to substantiate the obtained analytical findings.
In this paper, the famous Bernfeld–Haddock conjecture is generalized to a broader form combining with a class of non-autonomous delay differential equations. With the help of differential inequality technique and Dini derivative theory, it is proved that each solution of the addressed equations has boundedness and tends to a constant without requiring the delay feedback function to be strictly increasing, which greatly refines and extends the corresponding results in the existing literature. In particular, an explanatory example is performed to substantiate the obtained analytical findings.
关键词：
Boundary conditions;Boundary element method;Convergence of numerical methods;Discrete Fourier transforms;Fourier series;Galerkin methods;Hamiltonians;Iterative methods;Korteweg-de Vries equation;Runge Kutta methods;Blended iteration;Boussinesq;Energy;Energy preservation;Fourier-Galerkin methods;Hamiltonian boundary value methods;Highly accurate;KdV system;KdV-KdV system;Periodic boundary conditions;Ordinary differential equations
摘要：
In this paper, we propose a highly accurate scheme for two KdV systems of the Boussinesq type under periodic boundary conditions. The proposed scheme combines the Fourier-Galerkin method for spatial discretization with Hamiltonian boundary value methods for time integration, ensuring the conservation of discrete mass and energy. By expanding the system in Fourier series, the equations are firstly transformed into Hamiltonian form, preserving the original Hamiltonian structure. Applying the Fourier-Galerkin method for semi-discretization in space, we obtain a large-scale system of Hamiltonian ordinary differential equations, which is then solved using a class of energy-conserving Runge-Kutta methods, known as Hamiltonian boundary value methods. The efficiency of this approach is assessed, and several numerical examples are provided to demonstrate the effectiveness of the method.
In this paper, we propose a highly accurate scheme for two KdV systems of the Boussinesq type under periodic boundary conditions. The proposed scheme combines the Fourier-Galerkin method for spatial discretization with Hamiltonian boundary value methods for time integration, ensuring the conservation of discrete mass and energy. By expanding the system in Fourier series, the equations are firstly transformed into Hamiltonian form, preserving the original Hamiltonian structure. Applying the Fourier-Galerkin method for semi-discretization in space, we obtain a large-scale system of Hamiltonian ordinary differential equations, which is then solved using a class of energy-conserving Runge-Kutta methods, known as Hamiltonian boundary value methods. The efficiency of this approach is assessed, and several numerical examples are provided to demonstrate the effectiveness of the method.
摘要：
Sampled-data-based event-triggered (SDET) communication techniques have found extensive applications in the research of synchronization and consensus in directed networks (DNs). However, as the quantity of nodes in a network expands, existing investigations encounter difficulties in obtaining solutions within finite computation times due to computational complexity. For coping with this scenario, a novel event-triggered pinning quasi-synchronization approach is explored in this research for a category of switched directed networks (SDNs) with sampling measurements. By developing a time-dependent Lyapunov-Krasovskii functional (LKF) and implementing a state-dependent switching strategy utilizing sampling measurements, sufficient conditions are formulated to assure that the synchronization errors are ultimately bounded in an exponential fashion. Different from previous relevant findings, the verification of matrix conditions in the derived synchronization criterion no longer depends on the number of nodes in networks, making it more suitable for large-scale SDNs. Ultimately, two simulation examples are incorporated to elucidate the applicability of the newly crafted synchronization methodology.
摘要：
This paper focuses the initial boundary value problem to the compressible Oldroyd-B model in the two-dimensional space with vacuum. We establish a new blowup criterion in terms of parallel to rho parallel to L infinity tBMOx only. This work can be viewed as an extension of Lu and Zhang [Relative entropy, weak-strong uniqueness, and conditional regularity for a compressible Oldroyd-B model, SIAM J. Math. Anal., 50(2018), 557-590] where a blowup criterion involving the upper bound of the fluid density in the two-dimensional setting has been given.
摘要：
This paper is devoted to the study of a nonlocal diffusion competition model with unbounded free boundaries. It is assumed that two competing species initially occupy their respective unbounded habitats and exhibit a tendency to expand with a free boundary. As time progresses, the habitats of these two species gradually overlap, giving rise to competition within the shared habitat. For this free boundary problem with nonlocal diffusion, we establish the global existence and uniqueness of the solution and prove the spreading-vanishing dichotomy. Further, the asymptotic spreading speed is also determined.
This paper is devoted to the study of a nonlocal diffusion competition model with unbounded free boundaries. It is assumed that two competing species initially occupy their respective unbounded habitats and exhibit a tendency to expand with a free boundary. As time progresses, the habitats of these two species gradually overlap, giving rise to competition within the shared habitat. For this free boundary problem with nonlocal diffusion, we establish the global existence and uniqueness of the solution and prove the spreading-vanishing dichotomy. Further, the asymptotic spreading speed is also determined.
