Global Existence, Regularity, and Dissipativity of Reaction-diffusion Equations with State-dependent Delay and Supercritical Nonlinearities

This work aims to study the initial-boundary value problem of the reaction-diffusion equation ₜu-Δ u=f(u)+g(u(t-τ(t,uₜ)))+h(t,x) in a bounded domain with state-dependent delay and supercritical nonlinearities. We establish the global existence and discuss the regularity and dissipativity of the problem under weaker assumptions. In particular, the existence of a global pullback attractor is proved regardless of uniqueness.