UNBOUNDED SOLUTIONS OF THE NONLOCAL HEAT EQUATION

被引：17
|
作者：
Braendle, C. [1 ]
Chasseigne, E. [2 ]
Ferreira, R. [3 ]
机构：
[1] U Carlos III Madrid, Dept Matemat, Leganes 28911, Spain
[2] UF Rabelais Parc Grandmont, Lab Math & Phys Theor, F-37200 Tours, France
[3] U Complutense Madrid, Dept Matemat Aplicada, Madrid 28040, Spain
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2011年 / 10卷 / 06期
关键词：
Non-local diffusion; initial trace; optimal classes of data;
D O I：
10.3934/cpaa.2011.10.1663
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: u(t) = J * u - u, where J is a symmetric continuous probability density. Depending on the tail of J, we give a rather complete picture of the problem in optimal classes of data by: (i) estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a suitable class; (iii) proving blow-up in finite time in the case of some critical growths; (iv) giving explicit unbounded polynomial solutions.
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页码：1663 / 1686
页数：24
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