Existence for semilinear parabolic stochastic equations
type: Item
instance of: scholarly article
title: Existence for semilinear parabolic stochastic equations
zbMATH Open document ID: 1213.35260
DOI: 10.4171/RLM/579
author: Viorel Barbu
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2011-01-26T00:00:00Z
review text: The author considers the stochastic differential equation \(dX-\Delta Xdt+\beta(X) dt\ni\sqrt{Q}dW_{t}\) in \((0,T)\times G=Q_{T}\), \(X(0)=x\) in \(G\), \(X=0\) on \((0,T)\times\partial G=\Sigma_{T}\). Here \(G\) is an open and bounded subset of \(\mathbb R^{d}\) with smooth boundary \(\partial G\), \(d\geq1\), and \(W_{t}\) is a cylindrical Wiener process in \(L^2(G)=H\). The operator \(Q\in L(H,H)\) is self-adjoint, positive and of finite trace, \(\beta:\;\mathbb R\to2^{\mathbb R}\) is a maximal monotone graph everywhere defined on \(\mathbb R\). The author proves that under suitable assumptions on \(Q\), considered stochastic differential equation has a unique strong solution.
reviewed by: Aleksandr D. Borisenko
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 5841653
zbMATH Keywords: cylindrical Wiener process
zbMATH Keywords: mild solution
MaRDI profile type: Publication
cites work: Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
cites work: Kolmogorov equations for stochastic PDEs.
cites work: Stochastic Equations in Infinite Dimensions
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description: scientific article; zbMATH DE number 5841653