Existence, Non-existence, and Uniqueness for a Heat Equation with Exponential Nonlinearity in R2

被引：26

作者：

Ioku, Norisuke ^{[1
]}

Ruf, Bernhard ^{[2
]}

Terraneo, Elide ^{[2
]}

机构：

[1] Ehime Univ, Grad Sch Engn Sci, 2-5 Bunkyo Cho, Matsuyama, Ehime 7908577, Japan

[2] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2015年 / 18卷 / 01期

关键词：

Heat equation; Existence; Non-existence; Uniqueness; Critical nonlinearity; GLOBAL-SOLUTIONS; SCHRODINGER-EQUATIONS; PARABOLIC EQUATIONS; NONUNIQUENESS; INEQUALITY; SPACES; NLS;

D O I：

10.1007/s11040-015-9199-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a semilinear heat equation with exponential nonlinearity in R-2. We prove that local solutions do not exist for certain data in the Orlicz space exp L-2(R-2), even though a small data global existence result holds in the same space exp L-2(R-2). Moreover, some suitable subclass of exp L-2(R-2) for local existence and uniqueness is proposed.

引用

页数：19

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