Unbounded solutions of the nonlocal heat equation

2010/01/14 by Cristina Brändle, Brändle, Cristina, Emmanuel Chasseigne +3
Mathematics · #35A01 #35A02 #45A05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35A01 #msc:35A02 #msc:45A05

paper · pdf · doi:10.48550/arxiv.1001.2541

arxiv created 2010/02/25 · arxiv updated 2010/02/26

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.

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