拟线性退化抛物方程组解的整体存在和有限爆破  

Global existence and blow-up of solutions to quasilinear degenerate parabolic system

作　　者：王文海[1] 容跃堂[1] 薛应珍[1] 

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《青岛理工大学学报》2007年第1期99-102,120,共5页Journal of Qingdao University of Technology

摘　　要：研究了由三个拟线性退化抛物型方程通过非线性项耦合而得到的一类拟线性退化抛物方程组解的性质.该方程组描述了一个具有三种连续介质的燃烧过程及热扩散过程.通过运用比较定理和构造上、下解方法,建立了该方程组解的整体存在和有限爆破的充分条件.由此得到,当反应项和扩散项的指数满足不同条件时,方程组的解具有不同的性质.The properties of solution to a class of quasilinear degenerate parabolic system coupled via three nonlinear diffusion equation are considered. The processes of diffusion of heat and burning in three component continuous media with nonlinear conductivity and volume energy release are described by this system. By comparison theorem and the upper-lower solution method, the conditions for the global existence and the finite time blow-up of solution to the system are established. The solution of system has different properties when the exponential satisfied different conditions.

关 键 词：拟线性 退化抛物方程组 整体存在 有限爆破 

分 类 号：O175.26[理学—数学]