带梯度的抛物方程解的熄灭与区域的相关性

The Relation Between the Extinction of the Solution to the Parabolic Equation with Gradient Term and Its Domain

研究了半线性方程第一初边值问题解的熄灭性,通过引入辅助函数,应用重要积分,微分等式方法,对具零Dirichlet边界条件和具有一定初值的热方程,给出了1个导致解在有限时间内熄灭的与区域相关的充分条件,从而推广了已有的结论。

A class of semi-linear equation systems with the first imitial-value is concerned in the paper. By means of introducing auxiliary function, using important integratal as well as differential inequality, a sufficient condition below equation system with zero Dirichlet boundary is gotten,which lend the extinction of solution in finite time.