Blow‐up analysis for a system of heat equations coupled via nonlinear boundary conditions
Xianfa Song · Mathematical Methods in the Applied Sciences · 2007
Abstract In this paper, we study a system of heat equations $u_t=\Delta u, \, v_t=\Delta v\,{\rm in}\,\Omega\times(0,T)$ coupled via nonlinear boundary conditions Here p, q>0. We prove that the solutions always blow up in finite time for non‐trivial and non‐negative initial values. We also prove that the blow‐up occurs only on SR = ∂BR for Ω = BR = {x ϵ ℝn:|x|