Existence and multiplicity of self-similar solutions for heat equations with nonlinear boundary conditions

被引：11
|
作者：
Ferreira, Lucas C. F. [1 ]
Furtado, Marcelo F. [2 ]
Medeiros, Everaldo S. [3 ]
机构：
[1] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083859 Campinas, SP, Brazil
[2] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
[3] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 54卷 / 04期
基金：
巴西圣保罗研究基金会;
关键词：
WEIGHTED SOBOLEV SPACES; ASYMPTOTIC-BEHAVIOR; PARABOLIC EQUATIONS; CRITICAL EXPONENTS; BLOW-UP; NONUNIQUENESS; THEOREMS;
D O I：
10.1007/s00526-015-0931-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with self-similar solutions in the half-space for linear and semilinear heat equations with nonlinear boundary conditions. Existence, multiplicity and positivity of these solutions are analyzed. Self-similar profiles are obtained as solutions of a nonlinear elliptic PDE with drift term and a nonlinear Neummann boundary condition. For that, we employ a variational approach and derive some compact weighted embeddings for the trace operator.
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页码：4065 / 4078
页数：14
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