A triviality result for semilinear parabolic equations

被引：1

作者：

Castorina, Daniele ^{[1
]}

Catino, Giovanni ^{[2
]}

Mantegazza, Carlo ^{[1
]}

机构：

[1] Univ Napoli, Dipartimento Matemat & Applicaz, Via Cintia, I-80126 Naples, Italy

[2] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

来源：

MATHEMATICS IN ENGINEERING | 2022年 / 4卷 / 01期

关键词：

ancient solution; eternal solution; superlinear heat equation; LIOUVILLE-TYPE THEOREMS; SUPERLINEAR PROBLEMS; SINGULARITY;

D O I：

10.3934/mine.2022002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation u(t) = Delta u + vertical bar u vertical bar(p) on complete Riemannian manifolds of dimension n >= 5 with nonnegative Ricci tensor, when p is smaller than the critical Sobolev exponent n+2/n-2.

引用

页数：15

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