非线性抛物型方程初边值问题解的Blow up性质

BLOW UP PROPERTY OF THE SOLUTION FOR INITIAL-BOUNDARY VALUE PROBLEM OF NONLINEAR PARABOLIC EQUATIONS

本文研究一类非线性抛物型方程具有非线性边界条件的初边值问题.利用抛物型方程最大值原理和凸性方法证明了该问题的解在有限时间内爆破.推广了文献[7-9]的结果.

This paper deals with the initial-boundary value problem under the third nonlinear boundary condition for a kind of nonlinear parabolic equations. By applying the maximum value theory of parabolic equation and convex method, it is proved that the blow up of solution in a definite time under some assumed conditions. The conclusion popularizes the results of refernces [7-9].