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

Ruijing Wang, Desheng Li

This work aims to study the initial-boundary value problem of the reaction-diffusion equation $\pa_{t}u-Δu=f(u)+g(u(t-τ(t,u_t)))+h(t,x)$ in a bounded domain with state-dependent de…