The moment and almost surely exponential stability of stochastic heat equations

DOI10.1090/S0002-9939-08-09458-6zbMath1147.93395OpenAlexW1966158394MaRDI QIDQ3533880

Bin Xie

Publication date: 24 October 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-08-09458-6

zbMATH Keywords

exponential stabilitystochastic heat equationLyapunov exponent\(p\)-th momentalmost surely

Mathematics Subject Classification ID

Heat equation (35K05) Asymptotic stability in control theory (93D20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (7)

Lyapunov exponents of PDEs driven by fractional noise with Markovian switching ⋮ Stochastic heat equation: numerical positivity and almost surely exponential stability ⋮ Stability analysis of impulsive stochastic reaction-diffusion cellular neural network with distributed delay via fixed point theory ⋮ Impacts of Gaussian noises on the blow-up times of nonlinear stochastic partial differential equations ⋮ Lyapunov exponents of hybrid stochastic heat equations ⋮ \(p\)th moment exponential stability of nonlinear hybrid stochastic heat equations ⋮ Some effects of the noise intensity upon non-linear stochastic heat equations on \([0, 1\)]

Cites Work

• On the \(p\)th moment exponential stability criteria of neutral stochastic functional differential equations
• Stability of semilinear stochastic evolution equations
• Asymptotic stability of the linear Ito equation in infinite dimensions
• Stabilization of partial differential equations by noise
• Existence, uniqueness, and asymptotic behavior of mild solutions to stochastic functional differential equations in Hilbert spaces
• Exponential stability in \(p\)-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
• On stabilization of partial differential equations by noise
• On weak solutions of stochastic equations in Hilbert spaces
• Asymptotic stability theorems of semilinear stochastic evolution equations in hilbert spaces
• Stability of Infinite Dimensional Stochastic Differential Equations with Applications
• Stochastic Equations in Infinite Dimensions

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