一类交叉耦合抛物型方程组解的整体存在及爆破问题

研究一类交叉耦合非线性抛物型方程组解的整体存在问题以及解在有限时刻爆破问题,通过构造方程组的上、下解,得到解整体存在及解在有限时刻爆破的充分条件.对指数型和幂函数型混合的反应项和边界流采用常微分方法构造其上下解,而其它例如第一特征法运用于该方程就比较困难.

Global existence and blow-up problem of a class of nonlinear parabolic equations with cross coupling

The global existence and finite-instant blow-up problems of solutions to a class of nonlinear parabolic equations with cross-coupling were studied.By means of constructing upper-lower solutions to the equations,the sufficient conditions were obtained for global existence and finite-instant blow-up problems.As for the exponential reaction terms and boundary flow the ordinary differential equation method was used for about equation of constructing upper-lower solution.Other methods(for example the first eigen...