Article
A global solution for a reaction-diffusion equation on bounded domains
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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.
Keywords
non-autonomous reaction-diffusion equation, pullback global attractor, fractal dimension, Chafee-Infante equation, 35B40, 35B41, 35B45, 35K57, 37L30
Citation
Khellat, F. & Khormizi, M. B. (2018). A global solution for a reaction-diffusion equation on bounded domains. Applied Mathematics and Nonlinear Sciences, 3(1), 15–22. https://doi.org/10.21042/AMNS.2018.1.00002
F. Khellat and M. B. Khormizi, “A global solution for a reaction-diffusion equation on bounded domains,” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 1, pp. 15–22, 2018, doi: 10.21042/AMNS.2018.1.00002.
Khellat F, Khormizi MB. A global solution for a reaction-diffusion equation on bounded domains. Applied Mathematics and Nonlinear Sciences. 2018;3(1):15–22. doi:10.21042/AMNS.2018.1.00002.
Khellat, F. and Khormizi, M. B. (2018), ‘A global solution for a reaction-diffusion equation on bounded domains’, Applied Mathematics and Nonlinear Sciences, 3(1), pp. 15–22. Available at: https://doi.org/10.21042/AMNS.2018.1.00002.
Khellat, Farhad, and Mahmud Beyk Khormizi. “A Global Solution for a Reaction-diffusion Equation on Bounded Domains.” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 1, 2018, pp. 15–22. https://doi.org/10.21042/AMNS.2018.1.00002.
Khellat, Farhad, and Mahmud Beyk Khormizi. “A Global Solution for a Reaction-diffusion Equation on Bounded Domains.” Applied Mathematics and Nonlinear Sciences 3, no. 1 (2018): 15–22. https://doi.org/10.21042/AMNS.2018.1.00002.
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Published by: Engineering Journals
