Existence and regularity of pullback attractors for a non-autonomous diffusion equation with delay and nonlocal diffusion in time-dependent spaces

TL;DR

This paper investigates the long-term behavior of solutions to a complex non-autonomous diffusion equation with delay and nonlocal effects, establishing the existence and regularity of pullback attractors in time-dependent spaces.

Contribution

It proves the existence and regularity of pullback attractors for a non-autonomous diffusion equation with delay and nonlocal diffusion in time-dependent spaces, under polynomial growth conditions.

Findings

Existence of pullback attractors in time-dependent spaces.

Regularity results for the attractors.

Applicable to equations with hereditary and nonlocal effects.

Abstract

In this paper, we study the asymptotic behavior of solution to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space $C_{\mathcal{H}_{t}(\Omega)}$. When the nonlinear function $f$ satisfies the polynomial growth of arbitrary order $p-1$ $(p \ge 2)$ and the external force $h \in L_{l o c}^{2}\left(\mathbb{R} ; H^{-1}(\Omega)\right)$, we establish the existence and regularity of the time-dependent pullback attractors.