论文信息 - Asymptotic Behavior and Stability of Solutions of Semilinear Diffusion Equations

Asymptotic Behavior and Stability of Solutions of Semilinear Diffusion Equations

ByHiroshi MATANO*§ I. IntroductionThis paper is divided into two chapters. In the first chapter (§ 2^§ 4) we study the asymptotic behavior of solutions of semilinear diffu-sion equations — in particular their behavior around unstable equilibriumsolutions, so as to get a clearer understanding of the situation wherethose unstable equilibrium solutions are placed. The results will thenbe applied to making some stability criteria as well as to establishingtheorems on the existence of stable equilibrium solutions and on thestructure of multiple equilibrium solutions. In the second chapter (§ 5,§ 6) we are confined to Neumann problems and discuss the possibility ofthe existence of non-constant stable equilibrium solutions.Let D denote a bounded domain in R

Hiroshi Matano | H. Matano

[1] H. Amann. On the Existence of Positive Solutions of Nonlinear Elliptic Boundary value Problems , 1971 .

[2] Seizô Itô. A remark on my paper “A Boundary value problem of partial differential equations of parabolic type” in Duke Mathematical Journal , 1958 .

[3] H. Amann. Supersolutions, monotone iterations, and stability , 1976 .

[4] R. G. Casten,et al. Instability results for reaction diffusion equations with Neumann boundary conditions , 1978 .

[5] Seizô Itô,et al. Fundamental solutions of parabolic differential equations and boundary value problems , 1957 .

[6] Nathaniel Chafee,et al. Asymptotic behavior for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions , 1975 .

[7] H. Weinberger,et al. Maximum principles in differential equations , 1967 .

[8] H. B. Keller,et al. Elliptic boundary value problems suggested by nonlinear diffusion processes , 1969 .