Global Existence for Reaction-diffusion Equations with State-Dependent Delay and Fast-growing Nonlinearities
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911464308080640 |
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| author | Wang, Ruijing |
| author_facet | Wang, Ruijing |
| contents | This work aims to study the initial-boundary value problem of the reaction-diffusion equation with state-dependent delay $\pa_{t}u-Δu=f(u)+g(u,u(t-τ(t,u_t)))+h(t,x)$ in a bounded domain. We establish the global existence of the problem under suitable dissipative-type structural conditions, allowing both nonlinear terms $f$ and $g$ to have arbitrary polynomial growth rates. Another highlight in this work is that, we significantly relax the continuity assumptions imposed on the delay functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20473 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Existence for Reaction-diffusion Equations with State-Dependent Delay and Fast-growing Nonlinearities Wang, Ruijing Analysis of PDEs This work aims to study the initial-boundary value problem of the reaction-diffusion equation with state-dependent delay $\pa_{t}u-Δu=f(u)+g(u,u(t-τ(t,u_t)))+h(t,x)$ in a bounded domain. We establish the global existence of the problem under suitable dissipative-type structural conditions, allowing both nonlinear terms $f$ and $g$ to have arbitrary polynomial growth rates. Another highlight in this work is that, we significantly relax the continuity assumptions imposed on the delay functions. |
| title | Global Existence for Reaction-diffusion Equations with State-Dependent Delay and Fast-growing Nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.20473 |