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arXiv · 2610.15367

pper and Lower Bounds for Blow-up Times in Coupled Reaction--Diffusion Systems with Nonlocal Sources

Xin Zhao·Aynuer Ailatusi·Xianfa Song·Zeen Song
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Abstract

In this paper, we consider the following reaction-diffusion system \begin{equation*} \begin{cases} u_t=Δu+F\bigl(x,t,u,v,V(t)\bigr), & (x,t)\in\Om\times(0,T), v_t=Δv+G\bigl(x,t,u,v,U(t)\bigr), & (x,t)\in\Om\times(0,T), \mathcal B u=\mathcal B v=0, & (x,t)\in\partial\Om\times(0,T), u(x,0)=u_0(x),\quad v(x,0)=v_0(x), & x\in\Om, \end{cases} \end{equation*} where \begin{equation*} U(t)=\int_{\Om}u(x,t)\dd x,\qquad V(t)=\int_{\Om}v(x,t)\dd x, \end{equation*} and the boundary operator $\mathcal B$ is either \[ \mathcal B_D w=w \qquad\text{or}\qquad \mathcal B_N w=\partial_νw, \] $\Om\subset\R^N$ be a bounded domain with sufficiently smooth boundary, $N\ge 1$, and $ν$ is the outward unit normal on $\partial\Om$. Under certain conditions, we obtain the upper and lower bounds for the blowup time of the solution to the system.

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Xin Zhao, Aynuer Ailatusi, Xianfa Song, Zeen Song. 2026-10-11. pper and Lower Bounds for Blow-up Times in Coupled Reaction--Diffusion Systems with Nonlocal Sources. https://arxiv.org/abs/2610.15367

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