Attractors for a nonautonomous reaction-diffusion equation with delay-Reference-Cited by-同舟云学术

Attractors for a nonautonomous reaction-diffusion equation with delay

Published:2018-06-01 Issue:1 Volume:3 Page:127-150
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Harraga Hafidha¹,Yebdri Mustapha¹

Affiliation:

1. Department of Mathematics , University of Tlemcen , Tlemcen , 13000 , Algeria

Abstract

Abstract In this paper, we discuss the existence and uniqueness of solutions for a non-autonomous reaction-diffusion equation with delay, after we prove the existence of a pullback 𝒟-asymptotically compact process. By a priori estimates, we show that it has a pullback 𝒟-absorbing set that allow us to prove the existence of a pullback 𝒟-attractor for the associated process to the problem.

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.2018.1.00010

Reference9 articles.

1. T. Caraballo, J. Real. Attractors for 2D-Navier-Stokes models with delays. J. Differential Equations 205, 271-297 (2004). 10.1016/j.jde.2004.04.012

2. T. Caraballo, J. Real, G. Lukaszewicz. Pullback attractors for asymptotically compact nonautonomous dynamical systems. Nonlinear Anal. 64, 484-498 (2006). 10.1016/j.na.2005.03.111

3. J. Garcia-Luengo, P. Marin-Rubio. Reaction-diffusion equations with non-autonomous force in H–1and delays under measurability conditions on the driving delay term. J. Math.Anal.Appl. 417, 80-95 (2014). 10.1016/j.jmaa.2014.03.026

4. J. K. Hale, Asymptotic Behavior of Dissipative Systems. Mathematical Surveys and Monographs, AMS, Providence, RI, 25 (1988).

5. J. K. Hale, S. M. Verduyn-Lunel, Introduction to Functional Differential Equations. Springer-Verlag (1993).

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