期刊论文

Xie, Yongqin

英文

Journal of Mathematical Physics

0022-2488

2013

54

9

092701

10.1063/1.4818983

The authors are extremely grateful to Professor C. Sun and the anonymous reviewers for many helpful comments and suggestions that have contributed much to the improvement of this paper. This work was supported by the National Science and Technology Major Projects of China (Grant No. 2012ZX10001001-006), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 11A008), and the Science and Technology Innovation Project of Hunan for Graduate students (Grant No. CX2012B369).

本校为第一且通讯机构

We investigate the asymptotic behavior of solutions to a nonlinear reaction-diffusion equation with distribution derivatives in the inhomogeneous term. Because the solutions of this equation are not very regular, i.e., u only belongs to Lp(Rn)∩H1(Rn), and ut is only in H-1(Rn) for the forcing term in H-1(Rn), the standard method does not directly work in our case. We demonstrate the asymptotic regularity of the solution to obtain the (L2(Rn),H1(Rn))-asymptotic compactness of the semigroup and therefore the existence of a (L2(Rn),H1(Rn))-global...