STOCHASTIC DIFFERENTIAL EQUATIONS OF SOBOLEV TYPE IN INFINITE DIMENSIONAL HILBERT SPACES

In this work we present some results on the Cauchy problem for a general class of linear equations of Sobolev type with additive noise. We prove existence and uniqueness of mild and strong solutions using semigroup theory and properties of the stochastic convolution of a uniformly continuous semigro...

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Bibliographic Details
Published inMathematical Methods In Scattering Theory And Biomedical Engineering pp. 191 - 199
Main Authors LIASKOS, K. B., STRATIS, I. G., YANNACOPOULOS, A. N.
Format Book Chapter
LanguageEnglish
Published WORLD SCIENTIFIC 01.08.2006
Subjects
Applied Mathematics
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ISBN9812568603
9812773193
9789812773197
9789814477598
9814477591
9789812568601
DOI10.1142/9789812773197_0020

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Summary:In this work we present some results on the Cauchy problem for a general class of linear equations of Sobolev type with additive noise. We prove existence and uniqueness of mild and strong solutions using semigroup theory and properties of the stochastic convolution of a uniformly continuous semigroup generated by a linear and bounded operator. We also prove existence and uniqueness of mild and strong solutions for a perturbed Cauchy problem of Sobolev type and we investigate the continuity of the solution with respect to a small parameter ε > 0. As examples we study the standard Sobolev equation in bounded and unbounded domains, and a perturbed Cauchy problem for the heat equation.
ISBN:9812568603
9812773193
9789812773197
9789814477598
9814477591
9789812568601
DOI:10.1142/9789812773197_0020