Optimal and Sharp Convergence Rate of Solutions for a Semilinear Heat Equation with a Critical Exponent and Exponentially Approaching Initial Data

被引：1

作者：

Hoshino, Masaki ^{[1
]}

机构：

[1] Tohoku Gakuin Univ, Fac Liberal Arts, Dept Informat Sci, Sendai, Miyagi 9813193, Japan

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2024年 / 36卷 / 03期

关键词：

Cauchy problem; Semilinear heat equation; Stationary solution; Convergence; Critical exponent; Exponentially approaching; GROW-UP RATE; POSITIVE SOLUTIONS;

D O I：

10.1007/s10884-022-10198-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the behavior of solutions of the Cauchy problem for a semilinear heat equation with critical nonlinearity in the sense of Joseph and Lundgren. It is known that if two solutions are initially close enough near the spatial infinity, then these solutions approach each other. In this paper, we give its optimal and sharp convergence rate of solutions with a critical exponent and two exponentially approaching initial data. This rate contains a logarithmic term which does not contain in the super critical nonlinearity case. Proofs are given by a comparison method based on matched asymptotic expansion.

引用

页码：1981 / 2005

页数：25

共 45 条

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