A Compactness Tool for the Analysis of Nonlocal Evolution Equations

A Compactness Tool for the Analysis of Nonlocal Evolution Equations

In this paper we analyze the long time behavior of the solutions of a nonlocal diffusion-convection equation. We give a new compactness criterion in the Lebesgue spaces $L pi ((0,T)\times \Omega)$ and use it to obtain the first term in the asymptotic expansion of the solutions. Previous results of [...

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Veröffentlicht in:SIAM journal on mathematical analysis 2015-01, Vol.47 (2), p.1330-1354
Hauptverfasser: Ignat, Liviu I., Ignat, Tatiana I., Stancu-Dumitru, Denisa
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic expansions
Criteria
Diffusion
Evolution
Mathematical analysis
Partial differential equations
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Beschreibung
Zusammenfassung:In this paper we analyze the long time behavior of the solutions of a nonlocal diffusion-convection equation. We give a new compactness criterion in the Lebesgue spaces $L pi ((0,T)\times \Omega)$ and use it to obtain the first term in the asymptotic expansion of the solutions. Previous results of [J. Bourgain, H. Brezis, and P. Mironescu, in Optimal Control and Partial Differential Equations, IOS Press, Amsterdam, 2001] are used to obtain a compactness result in the spirit of the Aubin--Lions--Simon lemma.
ISSN:0036-1410
1095-7154
DOI:10.1137/130921349