Article
Attractors for a nonautonomous reaction-diffusion equation with delay
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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 π-asymptotically compact process. By a priori estimates, we show that it has a pullback π-absorbing set that allow us to prove the existence of a pullback π-attractor for the associated process to the problem.
Keywords
pullback attractors, nonclassical reaction-diffusion equations, critical exponent, delay term, 35B41, 35B40, Secondary 37L30, 35Q35
Citation
Harraga, H. & Yebdri, M. (2018). Attractors for a nonautonomous reaction-diffusion equation with delay. Applied Mathematics and Nonlinear Sciences, 3(1), 127β150. https://doi.org/10.21042/AMNS.2018.1.00010
H. Harraga and M. Yebdri, “Attractors for a nonautonomous reaction-diffusion equation with delay,” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 1, pp. 127β150, 2018, doi: 10.21042/AMNS.2018.1.00010.
Harraga H, Yebdri M. Attractors for a nonautonomous reaction-diffusion equation with delay. Applied Mathematics and Nonlinear Sciences. 2018;3(1):127β150. doi:10.21042/AMNS.2018.1.00010.
Harraga, H. and Yebdri, M. (2018), ‘Attractors for a nonautonomous reaction-diffusion equation with delay’, Applied Mathematics and Nonlinear Sciences, 3(1), pp. 127β150. Available at: https://doi.org/10.21042/AMNS.2018.1.00010.
Harraga, Hafidha, and Mustapha Yebdri. “Attractors for a Nonautonomous Reaction-diffusion Equation with Delay.” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 1, 2018, pp. 127β150. https://doi.org/10.21042/AMNS.2018.1.00010.
Harraga, Hafidha, and Mustapha Yebdri. “Attractors for a Nonautonomous Reaction-diffusion Equation with Delay.” Applied Mathematics and Nonlinear Sciences 3, no. 1 (2018): 127β150. https://doi.org/10.21042/AMNS.2018.1.00010.
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