Unbounded solutions of the nonlocal heat equation
Analysis of PDEs
2010-02-25 v2
Abstract
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) giving explicit unbounded polynomial solutions.
Keywords
Cite
@article{arxiv.1001.2541,
title = {Unbounded solutions of the nonlocal heat equation},
author = {Cristina Brändle and Emmanuel Chasseigne and Raul Ferreira},
journal= {arXiv preprint arXiv:1001.2541},
year = {2010}
}