Long-time behavior for a nonlocal convection diffusion equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Ignat, Liviu I.¹  Ignat, Tatiana I.¹ 

[1] Romanian Acad, Inst Math Simion Stoilow, 21 Calea Grivitei St, Bucharest 010702, Romania

关键词: Asymptotic behavior;    Nonlocal diffusion;    Nonlocal convection;   

DOI  :  10.1016/j.jmaa.2017.05.070

来源: Elsevier

【 摘 要 】

In this paper we consider a nonlocal viscous Burgers' equation and study the well-posedness and asymptotic behavior of its solutions. We prove that under the smallness assumption on the initial data the solutions behave as the self similar profiles of the Burgers' equation with Dirac mass as the initial datum. The first term in the asymptotic expansion of the solutions is obtained by rescaling the solutions and proving the compactness of their trajectories. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free