<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of mathematics, Faculty of mathematical sciences

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A global solution for a reaction-diffusion equation on bounded domains"}

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...

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

Published Online: Oct 03, 2018

Page range: 15 - 22

Received: Oct 26, 2017

Accepted: Feb 05, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00002

Keywords
non-autonomous reaction-diffusion equation, pullback global attractor, fractal dimension, Chafee-Infante equation

© 2018 Farhad Khellat and Mahmud Beyk Khormizi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Oct 03, 2018

Page range: 15 - 22

Received: Oct 26, 2017

Accepted: Feb 05, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00002

Keywordsnon-autonomous reaction-diffusion equation, pullback global attractor, fractal dimension, Chafee-Infante equation

© 2018 Farhad Khellat and Mahmud Beyk Khormizi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
non-autonomous reaction-diffusion equation, pullback global attractor, fractal dimension, Chafee-Infante equation