On Lr -regularity of global attractors generated by strong solutions of reaction-diffusion equations-Reference-Cited by-同舟云学术

On Lr -regularity of global attractors generated by strong solutions of reaction-diffusion equations

Published:2016-07-01 Issue:2 Volume:1 Page:375-390
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Valero José¹

Affiliation:

1. Centro de Investigación Operativa , Universidad Miguel Hernández , 03202 Elche , Alicante , Spain

Abstract

Abstract In this paper we prove that the global attractor generated by strong solutions of a reaction-diffusion equation without uniqueness of the Cauchy problem is bounded in suitable Lr -spaces. In order to obtain this result we prove first that the concepts of weak and mild solutions are equivalent under an appropriate assumption. Also, when the nonlinear term of the equation satisfies a supercritical growth condition the existence of a weak attractor is established.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.21042/AMNS.2016.2.00033

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