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arXiv · 2402.15996

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

Ruijing Wang·Desheng Li
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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.

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Ruijing Wang, Desheng Li. 2024-02-25. Global Existence, Regularity, and Dissipativity of Reaction-diffusion Equations with State-dependent Delay and Supercritical Nonlinearities. https://arxiv.org/abs/2402.15996

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