抛物方程解的完全爆破时间关于初值的依赖性

The Continuous Dependence on Initial Value of Complete Blow-up-time of Solutions for a Parabolic Equation

研究了一类抛物方程解的完全爆破时间关于初值的连续依赖性,其中方程源项为分段连续的函数.先利用椭圆型方程特征函数的相关性质给出了完全爆破时间与任意非爆破时间之间的关系,再运用有限覆盖定理及解的性质证明了结论.

The continuous dependence on initial value of complete blow-up-time of solutions of a class of parabolic equation was considered, in which the source item was piecewise continuous function. Firstly using the relative properties of the function on elliptic equation to give a relation between complete blow-up-time and any non-blow-up-time, then through the theorem of finite covering and the properties of solutions to prove the conclusion.