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arXiv · 1301.6019

A compactness tool for the analysis of nonlocal evolution equations

Liviu I. Ignat·Tatiana I. Ignat·Denisa Stancu-Dumitru
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Abstract

In this paper we give a new compactness criterion in the Lebesgue spaces $L^p((0,T)\times \Omega)$ and use it to obtain the first term in the asymptotic behaviour of the solutions of a nonlocal convection diffusion equation. We use previous results of Bourgain, Brezis and Mironescu to give a new criterion in the spirit of the Aubin-Lions-Simon Lemma.

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Liviu I. Ignat, Tatiana I. Ignat, Denisa Stancu-Dumitru. 2013-01-25. A compactness tool for the analysis of nonlocal evolution equations. https://arxiv.org/abs/1301.6019

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