一类具有局部化源和吸收项的抛物系统解的整体存在与爆破

Global Existence and Blow-up Properties for a Parabolic System with Localized Source and Absorption

在齐次Dirichlet边界条件研究如下抛物系统其中x_0(t):R^+→(0,a)是Holder连续函数;常数0≤α,β<1,p_1,p_2,q_1,q_2,k_1,k_2>0.利用正则化方法,在一定的假设条件下证明了经典解的存在性.接着利用比较原理证明了该系统正解的整体存在性和爆破性.最后给出了爆破解的精确爆破速率和爆破模式.

The aim of this paper is to investigate the following parabolic system under homogeneous Dirichlet boundary condition,where x_0（t）：R~＋→（0,a） is Holder continuous,and the constants 0≤α,β 1,p_1,p_2,q_1,q_2,k_1,k_2 0.Under appropriate hypotheses,we first prove the local existence of classical solution by a regularization method.Then we discuss the global existence and blow-up of positive solutions by using a comparison principle.Finally,we give the precise blow-up estimates and the uniform blow-up profiles.