PreprintCC BY 4.0arXiv
pper and Lower Bounds for Blow-up Times in Coupled Reaction--Diffusion Systems with Nonlocal Sources
Abstract
In this paper, we consider the following reaction-diffusion system ut=Δu+F(x,t,u,v,V(t)), & (x,t)∈Om×(0,T), vt=Δv+G(x,t,u,v,U(t)), & (x,t)∈Om×(0,T), ℬ u=ℬ v=0, & (x,t)∈∂Om×(0,T), u(x,0)=u0(x), v(x,0)=v0(x), & x∈Om, where U(t)=∫Omu(x,t)dd x, V(t)=∫Omv(x,t)dd x, and the boundary operator ℬ is either ℬD w=w or ℬN w=∂νw, Om⊂RN be a bounded domain with sufficiently smooth boundary, N≥ 1, and ν is the outward unit normal on ∂Om. Under certain conditions, we obtain the upper and lower bounds for the blowup time of the solution to the system.
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BibTeX
@misc{zhao2026pper,
title = {{pper and Lower Bounds for Blow-up Times in Coupled Reaction--Diffusion Systems with Nonlocal Sources}},
author = {Xin Zhao and Aynuer Ailatusi and Xianfa Song and Zeen Song},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15367},
eprint = {2610.15367},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15367},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - pper and Lower Bounds for Blow-up Times in Coupled Reaction--Diffusion Systems with Nonlocal Sources
AU - Xin Zhao
AU - Aynuer Ailatusi
AU - Xianfa Song
AU - Zeen Song
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15367
UR - https://arxiv.org/abs/2610.15367
AB - In this paper, we consider the following reaction-diffusion system u_t=Δu+F(x,t,u,v,V(t)), & (x,t)∈Om×(0,T), v_t=Δv+G(x,t,u,v,U(t)), & (x,t)∈Om×(0,T), ℬ u=ℬ v=0, & (x,t)∈∂Om×(0,T), u(x,0)=u_0(x), v(x,0)=v_0(x), & x∈Om, where U(t)=∫_Omu(x,t)dd x, V(t)=∫_Omv(x,t)dd x, and the boundary operator ℬ is either ℬ_D w=w or ℬ_N w=∂_νw, Om⊂R^N be a bounded domain with sufficiently smooth boundary, N≥ 1, and ν is the outward unit normal on ∂Om. Under certain conditions, we obtain the upper and lower bounds for the blowup time of the solution to the system.
ER -