LONG-TIME EXISTENCE FOR THE HEAT-EQUATION WITH A NOISE TERM

被引：44

作者：

MUELLER, C

机构：

[1] Department of Mathematics, University of Rochester, Rochester, 14627, NY

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1991年 / 90卷 / 04期

关键词：

D O I：

10.1007/BF01192141

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the equation u(t) = u(xx) + u(gamma) W for x on a finite interval, with Dirichlet boundary conditions. W is spacetime white noise. The initial condition is continuous and nonnegative. We show existence and uniqueness for all time, provided 1 less-than-or-equal-to gamma < 3/2.

引用

页码：505 / 517

页数：13