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

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 $\omega$-$\mathcal{D}$-limit compactness that allow us to prove the existence of the pullback $\mathcal{D}$-attractors for the associated process to the problem.

Keywords

• Pullback attractors
• nonclassical reaction-diffusion equations
• critical exponent, delay term