STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY PURELY SPATIAL NOISE

被引：25
|
作者：
Lototsky, Sergey V. [1 ]
Rozovskii, Boris L. [2 ]
机构：
[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA
[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2009年 / 41卷 / 04期
关键词：
generalized random elements; Malliavin calculus; Skorokhod integral; Wiener chaos; weighted spaces; SPACES; PDES;
D O I：
10.1137/070698440
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven by space-only noise. The paper presents results about solvability of such equations in weighted Wiener chaos spaces and studies the long-time behavior of the solutions of evolution equations with space-only noise.
引用
收藏
页码：1295 / 1322
页数：28
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