Strong solutions to stochastic wave equations with values in Riemannian manifolds

被引：34

作者：

Brzezniak, Zdzislaw ^{[1
]}

Ondrejat, Martin ^{[2
]}

机构：

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Acad Sci Czech Republic, Inst Math, CR-11567 Prague, Czech Republic

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2007年 / 253卷 / 02期

关键词：

stochastic wave equation; geometric wave equation;

D O I：

10.1016/j.jfa.2007.03.034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a d-dimensional compact Riemannian manifold. We prove existence of a unique global strong solution of the stochastic wave equation D-t partial derivative(t)u = D-x partial derivative(x)u + Y-u (partial derivative(t)u, partial derivative(x)u) V, where Y is a C-1-smooth transformation and W is a spatially homogeneous Wiener process on R whose spectral measure has finite moments up to order 2. (c) 2007 Published by Elsevier Inc.

引用

页码：449 / 481

页数：33

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