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.
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页码：5731 / 5773
页数：43
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