On exponential stability criteria of stochastic partial differential equations
type: Item
instance of: scholarly article
title: On exponential stability criteria of stochastic partial differential equations
zbMATH Open document ID: 0997.60065
DOI: 10.1016/S0304-4149(99)00045-9
author: Kai Liu
author: T. Caraballo
published in: Stochastic Processes and their Applications
publication date: 2002-08-29T00:00:00Z
review text: Some criteria for the mean square and almost sure exponential stability of the zero solution of the nonlinear stochastic partial differential equation \[ X_t=X_0+\int _0^tA(s,X_s) ds + \int _0^tB(s,X_s) dW_s \] are given, where \(A(t,\cdot): V\to V'\), \(B(t,\cdot):V\to \mathcal L(K,H)\), \(V\) is a Banach space and \(H,K\) are real separable Banach spaces such that \(V\hookrightarrow H=H'\hookrightarrow V'\), where the injections are continuous and dense. The coefficients \(A,B\) are assumed to satisfy the usual coercivity, boundedness, monotonicity, hemicontinuity and measurability conditions. The main results obtained by \textit{T. Caraballo} and \textit{J. Real} [Stochastic Anal. Appl. 12, No. 5, 517-525 (1994; Zbl 0808.93069)] are improved, which in particular concerns the case of non-autonomous equation. Several illustrating examples are also given.
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 1792542
zbMATH Keywords: exponential stability
zbMATH Keywords: stochastic partial differential equations
MaRDI profile type: Publication
cites work: On the pathwise exponential stability of non–linear stochastic partial differential equations
cites work: Stability of nonlinear stochastic-evolution equations
cites work: Asymptotic stability of the linear Ito equation in infinite dimensions
cites work: Q4303533
full work available at URL: s0304-4149(99)00045-9
OpenAlex ID: W2110068264
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description: scientific article; zbMATH DE number 1792542