作者机构：
[Li, Jianliang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.
通讯机构：
[Li, Jianliang] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.
关键词：
Inverse acoustic scattering;generalized impedance boundary condition;reverse time migration method;35J05;65N21;65R32;78A46
摘要：
We consider the inverse scattering problem of determining the shape of an impenetrable two-dimensional obstacle with a generalized impedance boundary condition from near-field measurements. We propose the reverse time migration method where the imaging functional is defined as the imaginary part of the cross-correlation. Our analysis shows that, on the one hand, the imaging functional has contrast at the boundary of the scatterer and decays outside the scatterer; On the other hand, the imaging functional is always positive thus may have better stability properties. These imply that the approach has powerful imaging quality which is confirmed in our numerical experiments.
摘要：
<jats:title>Abstract</jats:title><jats:p>In this paper, we mainly investigate upper semicontinuity and regularity of attractors for nonclassical diffusion equations with perturbed parameters<jats:italic>ν</jats:italic>and the nonlinear term<jats:italic>f</jats:italic>satisfying the polynomial growth of arbitrary order<jats:inline-formula><jats:alternatives><jats:tex-math>$p-1$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:math></jats:alternatives></jats:inline-formula>(<jats:inline-formula><jats:alternatives><jats:tex-math>$p \geq 2$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math></jats:alternatives></jats:inline-formula>). We extend the asymptotic a priori estimate method (see (Wang et al. in Appl. Math. Comput. 240:51–61, 2014)) to verify asymptotic compactness and upper semicontinuity of a family of semigroups for autonomous dynamical systems (see Theorems 2.2 and 2.3). By using the new operator decomposition method, we construct asymptotic contractive function and obtain the upper semicontinuity for our problem, which generalizes the results obtained in (Wang et al. in Appl. Math. Comput. 240:51–61, 2014). In particular, the regularity of global attractors is obtained, which extends and improves some results in (Xie et al. in J. Funct. Spaces 2016:5340489, 2016; Xie et al. in Nonlinear Anal. 31:23–37, 2016).</jats:p>
通讯机构：
[Gong, Hongfang] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
关键词：
Petri nets;Fault detection;Test pattern generators;Boolean functions;Software;Licenses;Automatic test cases generation;fault-based testing;general Boolean expression test;ordered binary label-driven Petri net;path-oriented test criteria
摘要：
Boolean expression testing requires certain types of tests for each Boolean expression in program specification or implementation. Fault-based testing essentially uses a subset of the exhaustive test set to detect certain special types of faults. A fault-based Boolean expression testing strategy called constraint true and false test point (CTFTP) is proposed. The test consists of two test case generation strategies, namely a unique constraint true point (UCTP) strategy and a near constraint false point (NCFP) strategy. An ordered binary label-driven Petri net model is presented to analyze the interaction between Boolean transitions and Boolean literals and yield the test paths of a singular term for the irredundant disjunctive normal forms (IDNFs). On the basis of the test paths, we develop a configuration-based IDNF test generation algorithm, which is employed to obtain the UCTP, NCFP, and CTFTP test sets for the IDNFs. The proposed test generation algorithm based on literal substitution is applied to extend the CTFTP strategy and generate a test suite for general Boolean expressions, which are evaluated using TCAS II specifications. Experimental results show that the CTFTP strategy can detect the same seven types of faults similar to the MUMCUT strategy when testing IDNFs, but only a subset of the MUMCUT test set is required. Five types of faults of general Boolean expressions can also be detected using CTFTP strategies.
期刊：
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2020年16(1):325-356 ISSN：1547-5816
通讯作者：
Ying, J.
作者机构：
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, China;School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, China
通讯机构：
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
关键词：
Biomolecular electrostatics;Block iteration method;Finite element method;Implicit continuum model;Nonlocal model
期刊：
Communications in Partial Differential Equations,2020年45(10):1335-1380 ISSN：0360-5302
通讯作者：
Li, Peijun
作者机构：
[Li, Jianliang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.;[Helin, Tapio] LUT Univ, Sch Engn Sci, Lappeenranta, Finland.;[Li, Peijun] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA.
通讯机构：
[Li, Peijun] P;Purdue Univ, Dept Math, W Lafayette, IN 47907 USA.
关键词：
Elastic wave equation;Gaussian random function;Helmholtz equation;inverse source problem;uniqueness
摘要：
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a domain away from the source region. The source is assumed to be a microlocally isotropic generalized Gaussian random function such that its covariance operator is a classical pseudo-differential operator. Given such a distributional source, the direct problem is shown to have a unique solution by using an integral equation approach and the Sobolev embedding theorem. For the inverse problem, we demonstrate that the amplitude of the scattering field averaged over the frequency band, obtained from a single realization of the random source, determines uniquely the principle symbol of the covariance operator. The analysis employs asymptotic expansions of the Green functions and microlocal analysis of the Fourier integral operators associated with the Helmholtz and Navier equations.
关键词：
Helmholtz equation;Inverse scattering;locally rough interface;the Kirsch-Kress approach;transmission problem
摘要：
This paper is concerned with the inverse problem of reconstructing an infinite, locally rough interface from the scattered field measured on line segments above and below the interface in two dimensions. We extend the Kirsch-Kress method originally developed for inverse obstacle scattering problems to the above inverse transmission problem with unbounded interfaces. To this end, we reformulate our inverse problem as a nonlinear optimization problem with a Tikhonov regularization term. We prove the convergence of the optimization problem when the regularization parameter tends to zero. Finally, numerical experiments are carried out to show the validity of the inversion algorithm.
摘要：
In this paper, we consider a type of fractional diffusion equation (FDE) with variable coefficients on a finite domain. Firstly, we utilize a second-order scheme to approximate the Riemann-Liouville fractional derivative and present the finite difference scheme. Specifically, we discuss the Crank-Nicolson scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the scheme and conclude that the scheme is unconditionally stable and convergent with the second -order accuracy of theta(tau(2) + h(2)). Furthermore, we develop a fast accurate iterative method for the Crank-Nicolson scheme, which only requires storage of theta(m) and computational cost of theta(m log m) while retaining the same accuracy and approximation property as Gauss elimination, where m = 1/h is the partition number in space direction. Finally, several numerical examples are given to show the effectiveness of the numerical method, and the results are in excellent agreement with the theoretical analysis. (C) 2016 Elsevier Ltd. All rights reserved.
