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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Année : 2014

Isothermalization for a Non-local Heat Equation

Résumé

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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Dates et versions

hal-00441672 , version 1 (17-12-2009)
hal-00441672 , version 2 (05-12-2011)

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Citer

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