Initial trace of solutions of semilinear heat equations with absorption

被引：3

作者：

Al Sayed, Waad ^{[1
]}

Veron, Laurent ^{[2
]}

机构：

[1] Fahad Bin Sultan Univ, Coll Sci & Humanities, Tabuk, Saudi Arabia

[2] Univ Tours, Dept Math, Tours, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2013年 / 93卷

关键词：

Heat equation; Singularities; Harnack inequalities; Radon measures; Borel measures; Barrier; Initial trace; PARABOLIC EQUATIONS; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; BOUNDARY; SINGULARITIES; DIFFUSION;

D O I：

10.1016/j.na.2013.07.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the initial trace problem for positive solutions of semilinear heat equations with strong absorption. We show that in general this initial trace is an outer regular Borel measure. We emphasize in particular the case where u satisfies (E) partial derivative(t)u - Delta u + t(alpha)vertical bar u vertical bar(q-1) u = 0, with q > 1 and alpha > -1 and prove that in the subcritical case 1 < q < q(alpha,N) := 1 + 2(1 + alpha)/N the initial trace establishes a one to one correspondence between the set of outer regular Borel measures in R-N and the set of positive solutions of (E) in R-N x R+. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：197 / 225

页数：29

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