INITIAL TRACES AND SOLVABILITY FOR A SEMILINEAR HEAT EQUATION ON A HALF SPACE OF RN

被引：4

作者：

Hisa, Kotaro ^{[1
]}

Ishige, Kazuhiro ^{[2
]}

Takahashi, Jin ^{[3
]}

机构：

[1] Tohoku Univ, Math Inst, 6-3 Aoba,Aoba ku, Sendai 9808578, Japan

[2] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba,Meguro ku, Tokyo 1538914, Japan

[3] Tokyo Inst Technol, Dept Math & Comp Sci, 2-12-1 Ookayama,Meguro ku, Tokyo 1528552, Japan

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 376卷 / 08期

基金：

日本学术振兴会;

关键词：

Initial trace; semilinear heat equation; Cauchy-Dirichlet problem; solvability; NONLINEAR BOUNDARY-CONDITION; LINEAR PARABOLIC EQUATIONS; CAUCHY-PROBLEM; CRITICAL EXPONENTS; POSITIVE SOLUTIONS; LOCAL EXISTENCE; BLOW-UP; NONEXISTENCE; SUPERSOLUTIONS;

D O I：

10.1090/tran/8922

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show the existence and the uniqueness of initial traces of non -negative solutions to a semilinear heat equation on a half space of RN under the zero Dirichlet boundary condition. Furthermore, we obtain necessary con-ditions and sufficient conditions on the initial data for the solvability of the corresponding Cauchy-Dirichlet problem. Our necessary conditions and suffi-cient conditions are sharp and enable us to find optimal singularities of initial data for the solvability of the Cauchy-Dirichlet problem.

引用

页码：5731 / 5773

页数：43

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