Electron. J. Diff. Equ., Vol. 2016 (2016), No. 07, pp. 1-33.

Pullback attractors for a class of semilinear nonclassical diffusion equations with delay

Hafidha Harraga, Mustapha Yebdri

Abstract:
In this article, we analyze the existence of solutions for a nonclassical reaction-diffusion equation with critical nonlinearity, a time-dependent force with exponential growth and delayed force term, where the delay term can be entrained by a function under assumptions of measurability. Using a priori estimates we obtain the pullback $\mathcal{D}$-absorbing process and the pullback $\omega\text{-}\mathcal{D}$-limit compactness that allow us to prove the existence of the pullback $\mathcal{D}$-attractors for the associated process to the problem.

Submitted June 4, 2015. Published January 6, 2016.
Math Subject Classifications: 35R10, 35K57, 35B41.
Key Words: Pullback attractors; nonclassical reaction-diffusion equations; critical exponent, delay term.

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Hafidha Harraga
Dept of Mathematics
University Aboubekr Belkaid ot Tlemcen 13000
Tlemcen, Algeria
email: h.harraga@yahoo.fr
Mustapha Yebdri
Dept of Mathematics
University Aboubekr Belkaid ot Tlemcen 13000
Tlemcen, Algeria
email: yebdri@yahoo.com

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