A global solution for a reaction-diffusion equation on bounded domains-Reference-Cited by-同舟云学术

A global solution for a reaction-diffusion equation on bounded domains

Published:2018-06-01 Issue:1 Volume:3 Page:15-22
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Khellat Farhad¹,Khormizi Mahmud Beyk¹

Affiliation:

1. Department of mathematics, Faculty of mathematical sciences , Shahid Beheshti University , Tehran , Iran

Abstract

Abstract In the literature, it has been proved the existence of a pullback global attractor for reaction-diffusion equation on a bounded domain and under some conditions, a uniform bound on the dimension of its sections. Using those results and putting a bound on the diameter of the domain, we proved that the pullback global attractor consists only of one global solution. As an application to this result, a bounded perturbation of Chafee-Infante equation has been studied.

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.2018.1.00002

Reference12 articles.

1. Caraballo, T., Langa, JA & Valero, J. (2003) “The dimension of attractors of nonautonomous partial differential equations,” The ANZIAM Journal, 45, pp. 207–222, 10.1017/S1446181100013274

2. Carvalho, A. N., Langa, JA & Robinson, J. (2012) “Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation,” Proc. Amer. Math. Soc. 140, pp. 2357–2373, 10.1090/S0002-9939-2011-11071-2

3. Carvalho, A. N., Langa, JA & Robinson, J. (2012) Attractors for infinite-dimensional non-autonomous dynamical systems, 1st Ed. (Springer Science & Business Media, USA).

4. Carvalho, A. N. & Sonner, S. (2013) “Pullback exponential attractors for evolution processes in Banach spaces: Theoretical results,” Commun. Pure Appl. Anal12, pp. 3047–3071, 10.3934/cpaa.2013.12.3047

5. Carvalho, A. N. & Sonner, S. (2014) “Pullback exponential attractors for evolution processes in Banach spaces: properties and applications,” Commun. Pure Appl. Anal3, pp. 1141–1165, 10.3934/cpaa.2014.13.1141

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