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

页码：1295 / 1322

页数：28

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