Observability Estimates and Null Controllability for Forward and Backward Linear Stochastic Kuramoto--Sivashinsky Equations

DOI10.1137/130943820zbMath1312.93018OpenAlexW2009127884MaRDI QIDQ5252492

Peng Gao, Mo Chen, Yong Li

Publication date: 2 June 2015

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/130943820

zbMATH Keywords

null controllabilityCarleman estimateobservability estimateforward and backward linear stochastic Kuramoto-Sivashinsky equations

Mathematics Subject Classification ID

Controllability (93B05) Observability (93B07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Higher-order parabolic equations (35K25)

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Cites Work

• Unnamed Item
• Local exact controllability to the trajectories of the 1-D Kuramoto-Sivashinsky equation
• On the stochastic wave equation with nonlinear damping
• Carleman estimates and controllability of linear stochastic heat equations
• Approximate controllability of a stochastic wave equation
• Observability estimate and null controllability for one-dimensional fourth order parabolic equation
• Exact controllability for stochastic Schrödinger equations
• On the stochastic porous medium equation
• Lipschitz stability in an inverse problem for the Kuramoto–Sivashinsky equation
• Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems
• CARLEMAN ESTIMATE AND UNIQUE CONTINUATION PROPERTY FOR THE LINEAR STOCHASTIC KORTEWEG–DE VRIES EQUATION
• Null Controllability for Forward and Backward Stochastic Parabolic Equations
• Carleman and Observability Estimates for Stochastic Wave Equations
• Nonlinear instability at the interface between two viscous fluids
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• Stability of the kuramoto‐sivashinsky and related systems
• An Introduction to Partial Differential Equations
• Observability Estimate for Stochastic Schrödinger Equations and Its Applications
• Exact Controllability for Stochastic Transport Equations
• Observability Estimate and State Observation Problems for Stochastic Hyperbolic Equations

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