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Article . 1995 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1995
Data sources: zbMATH Open
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Stochastic partial differential equations in M-type 2 Banach spaces

Stochastic partial differential equations in \(M\)-type 2 Banach spaces
Authors: Brzeźniak, Zdzisław;

Stochastic partial differential equations in M-type 2 Banach spaces

Abstract

The author proves an existence and uniqueness theorem for a stochastic differential equation in \(M\)-type 2 Banach spaces of the following type \[ du(t) + Au(t)dt = \sum B^j u(t) dw^j(t) + f(t), \quad u(0) = u_0, \] where \(- A\) is a generator of an analytic semigroup \(\{e^{- tA}\}_{r \geq 0}\) on \(X\), an \(M\)-type 2 Banach space, \(B^1, \ldots, B^d\) are linear operators in \(X\) and \(w(t)\) is a \(d\)-dimensional Wiener process. The author considers the case, when the space of initial conditions is some real interpolation space between the domain of \(A\) and \(X\), and the case, when the space of initial conditions is \(X\). Also the author considers the case, when \(X\) is a Hilbert space and applies the obtained results to stochastic parabolic equations.

Related Organizations
Keywords

stochastic parabolic equations, Stochastic partial differential equations (aspects of stochastic analysis), One-parameter semigroups and linear evolution equations, General theory of partial differential operators, existence, uniqueness, PDEs with randomness, stochastic partial differential equations, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, space of initial conditions

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
97
Top 10%
Top 1%
Average
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