一类非线性抛物型方程组解的整体存在及爆破

Global existence and blow up for a nonlinear parabolic equations

研究了一类带有非线性边界条件的非线性抛物型方程组解的整体存在及解在有限时刻爆破问题.通过构造方程组的上、下解.得到了解整体存在及解在有限时刻爆破的充分条件.对指数型反应项和边界流采用了常微分方程方法构造其上下解,而其它例如第一特征值等方法运用于该方程就比较困难.

The globa existence and when blow up problem for solutions of a parabolic equations with nonlinear boundary conditions are studied. Using the method of upper-under solutions of the euqations. Two sufficient conditions for the global existence and blow up problem are obtained. Results constructing upper-lower solution by ordinary differential equation about equation of exponential reaction terns and boundary flow, but other methods （for example the first eigenvalue etc） are more difficult of the equation.