Isothermalization for a Non-local Heat Equation

2009/12/17 by Emmanuel Chasseigne, Chasseigne, Emmanuel, Raul Ferreira +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.0912.3332

arxiv created 2011/12/05 · arxiv updated 2011/12/06

Abstract

n this paper we study the asymptotic behavior for a nonlocal heat equation in an inhomogenous medium: ρ(x)u_t=J∗ u-u inℝ^N× (0,∞) , where ρ 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 u₀ and ρ, we prove various isothermalisation results, i.e. u(t) converges to a constant state in the whole space.

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