一类具非局部边界条件的拟线性抛物方程解的整体存在与爆破

摘要

This paper deals with the global existence and blow-up of solutions to a quasi-linear parabolic equation u1 ＝ f(u)(Δ u + a∫n u(y,t)dy-u) with nonlocal boundary condition u(x,t)=∫nk(x,y)u(y,t)dy on(a)Ω where Ω is a bounded domain in RN with smooth boundary (a)Ω.Under some hypotheses on f(s) and k(x,y),we gave sufficient conditions for the finite time blow-up or global existence of solutions.In addition,the blow-up rate of solutions was derived for a special case.%考虑拟线性方程u1＝f(u)(△u+a∫Ωu(y,t)dy－u)在非局部边界条件u(x,t)＝∫Ωκ(x,y)u(y,t)dy(x∈(a)Ω)下解的整体存在与爆破,其中Ω是RN中具光滑边界的有界区域.通过对扩散系数f(s)和权函数k(x,y)加适当条件,给出了解整体存在或爆破的充分条件,并得到了一定条件下解的爆破速率估计.