Blow-up analysis for a system of heat equations coupled via nonlinear boundary conditions

摘要

In this paper; we study a system of heat equations u(t) = Delta u, v(t) = Delta v in Omega x (0, T) coupled via nonlinear boundary conditions partial derivative u/partial derivative eta = e(pv), partial derivative v/partial derivative eta = u(q) on partial derivative Omega x (0, T) 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 S-R = partial derivative B-R for Omega = B-R = {x is an element of R-n : vertical bar x vertical bar < R} and C-1(T-t)(-1/2q) <= u(R,t) <= C-2(T-t)(-1/2q), log(C-3(T-t)(-(q+1)/2pq)) <= v(R, t) <= log(C-4(T-t)(-(q+1)/2pq)) under some assumptions on the initial values. Copyright (c) 2007 John Wiley & Sons, Ltd.