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

Ruijing Wang; Desheng Li

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

Analysis of PDEs 2024-02-27 v1 Dynamical Systems

Authors: Ruijing Wang , Desheng Li

Abstract

This work aims to study the initial-boundary value problem of the reaction-diffusion equation $\pa_{t}u-\Delta u=f(u)+g(u(t-\tau(t,u_t)))+h(t,x)$ 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.

Keywords

reaction-diffusion equations state-dependent delay supercritical nonlinearities global existence regularity dissipativity global pullback attractor

Cite

@article{arxiv.2402.15996,
  title  = {Global Existence, Regularity, and Dissipativity of Reaction-diffusion Equations with State-dependent Delay and Supercritical Nonlinearities},
  author = {Ruijing Wang and Desheng Li},
  journal= {arXiv preprint arXiv:2402.15996},
  year   = {2024}
}

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