含奇异项的退缩抛物型方程解的猝灭现象

Quenching for singular and degenerate parabolic equation

考虑含奇异项的退缩抛物型方程的初边值问题,给出了解的局部存在性与惟一性.当区域适当大时,即当所考虑区域上的Laplace算子在Dirichlet边界条件下的第一特征值小于1时,对于奇异项的两种不同情形,分别证明解会在有限时刻发生猝灭现象.

<Abstrcat>A class singular and degenerate parabolic equation is considered. The local existence and uniqueness are proved. Moreover, in two different singular cases the solution will quench in a finite time on an adequate large region on which the first eigenvalue of Laplace operator with Dirichlet boundary conditions is smaller than 1.