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

被引：0
|
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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