# Isothermalization for a Non-local Heat Equation

Abstract : n this paper we study the asymptotic behavior for a nonlocal heat equation in an inhomogenous medium: $\rho(x)u_t=J\ast u-u \text{ in }\mathbb{R}^N\times (0,\infty)\,,$ where $\rho$ is a continous positive function, $u$ is nonnegative and $J$ is a probability measure having finite second-order momentum. Depending on integrability conditions on the initial data $u_0$ and $\rho$, we prove various isothermalisation results, i.e. $u(t)$ converges to a constant state in the whole space.
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Cited literature [7 references]

https://hal.archives-ouvertes.fr/hal-00441672
Contributor : Emmanuel Chasseigne <>
Submitted on : Monday, December 5, 2011 - 3:19:49 PM
Last modification on : Thursday, January 9, 2020 - 6:26:03 PM
Document(s) archivé(s) le : Tuesday, March 6, 2012 - 2:35:42 AM

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### Identifiers

• HAL Id : hal-00441672, version 2
• ARXIV : 0912.3332

### Citation

Emmanuel Chasseigne, Raul Ferreira. Isothermalization for a Non-local Heat Equation. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2014, 13, pp.1-18. ⟨hal-00441672v2⟩

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