Asymptotic convergence of solutions for Laplace reaction-diffusion equations

被引：0
|
作者：
Iwasaki, Satoru [1 ]
Yagi, Atsushi [2 ]
机构：
[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Informat & Phys Sci, Suita, Osaka 5650871, Japan
[2] Osaka Univ, Grad Sch Informat Sci & Technol, Suita, Osaka 5650871, Japan
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2020年 / 51卷
关键词：
Diffusion equations in composite media; Lojasiewicz-Simon inequality; Asymptotic convergence; TRANSIENT CONDUCTION; GRADIENT INEQUALITY; COMPOSITE SLAB;
D O I：
10.1016/j.nonrwa.2019.102986
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the initial-boundary value problem for a Laplace reaction-diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show asymptotic convergence of bounded global solutions if they exist under the assumption that the reaction function is analytic in neighborhoods of their w-limit sets. Reduction of degenerate evolution equation to multivalued evolution equation enables us to use the theory of the infinite-dimensional Lojasiewicz-Simon gradient inequality. (C) 2019 The Authors. Published by Elsevier Ltd.
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页数：21
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