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Unbounded solutions of the nonlocal heat equation

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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Submitted on : Thursday, February 25, 2010 - 8:23:51 AM
Last modification on : Monday, June 1, 2020 - 9:12:03 AM
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  • HAL Id : hal-00447374, version 2
  • ARXIV : 1001.2541

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Cristina Brändle, Emmanuel Chasseigne, Raul Ferreira. Unbounded solutions of the nonlocal heat equation. Communications on Pure and Applied Analysis, AIMS American Institute of Mathematical Sciences, 2011, 10, pp.1663-1686. ⟨hal-00447374v2⟩

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