On the local existence for Hardy parabolic equations with singular initial data

被引：1

作者：

Castillo, Ricardo ^{[1
]}

Guzman-Rea, Omar ^{[2
]}

Loayza, Miguel ^{[2
]}

机构：

[1] Univ Bio Bio, Dept Matemat, Concepcion, Chile

[2] Univ Fed Pernambuco UFPE, Dept Matemat, Recife, PE, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 510卷 / 02期

关键词：

Heat equation; Singular potential; Local existence; Non-existence; Singular initial data; GLOBAL-SOLUTIONS; HEAT-EQUATIONS; NONEXISTENCE;

D O I：

10.1016/j.jmaa.2022.126022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the singular nonlinear equation u(t) - Delta u = vertical bar.vertical bar(-gamma) f(u) in Omega x (0, T) with gamma > 0 and Dirichlet conditions on the boundary. This equation is known in the literature as a Hardy parabolic equation. The function f : [0, infinity) -> [0, infinity) is continuous and non-decreasing, and Omega is either a smooth bounded domain containing the origin or the whole space R-N. We determine necessary and sufficient conditions for the existence and non-existence of solutions for initial data u(0) is an element of L-r(Omega), u(0) >= 0, with 1 <= r < infinity. We also give a uniqueness result. (C) 2022 Elsevier Inc. All rights reserved.

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页数：29

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