A Delay Nonlocal Quasilinear Chafee–Infante Problem: An Approach via Semigroup Theory

Abstract

In this work we study a dissipative one dimensional scalar parabolic problem with non-local nonlinear diffusion with delay. We consider the general situation in which the functions involved are only continuous and solutions may not be unique. We establish conditions for global existence and prove the existence of global attractors. All results are presented only in the autonomous since the non-autonomous case follows in the same way, including the existence of pullback attractors. A particularly interesting feature is that there is a semilinear problem (nonlocal in space and in time) from which one can obtain all solutions of the associated quasilinear problem and that for this semilinear problem the delay depends on the initial function making its study more involved.