Conditional stability in determination of initial data for stochastic parabolic equations

DOI10.1088/1361-6420/aa5d7azbMath1372.35374OpenAlexW2585502697MaRDI QIDQ2977558

Ganghua Yuan

Publication date: 18 April 2017

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6420/aa5d7a

zbMATH Keywords

conditional stabilityCarleman estimatebackward heat problemstochastic parabolic equation

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) PDEs with randomness, stochastic partial differential equations (35R60) Second-order parabolic equations (35K10)

Related Items (12)

Simultaneous recoveries for semilinear parabolic systems ⋮ Determination of the solution of a stochastic parabolic equation by the terminal value ⋮ Two Multiobjective Problems for Stochastic Degenerate Parabolic Equations ⋮ A numerical method for a backward problem of a linear stochastic Kuramoto-Sivashinsky equation ⋮ An inverse potential problem for the stochastic diffusion equation with a multiplicative white noise ⋮ Hardy’s uncertainty principle and unique continuation property for stochastic heat equations ⋮ Global uniqueness in an inverse problem for a class of damped stochastic plate equations ⋮ On terminal value problems for bi-parabolic equations driven by Wiener process and fractional Brownian motions ⋮ Identification of a time-dependent control parameter for a stochastic diffusion equation ⋮ Carleman Estimates of Some Stochastic Degenerate Parabolic Equations and Application ⋮ A concise introduction to control theory for stochastic partial differential equations ⋮ On a stochastic nonclassical diffusion equation with standard and fractional Brownian motion

Cites Work

• Infinite dimensional parameter identification for stochastic parabolic systems
• Sharp adaptation for inverse problems with random noise
• Carleman estimates for coefficient inverse problems and numerical applications.
• Conditional stability and numerical reconstruction of initial temperature
• Simultaneous reconstruction of the initial temperature and heat radiative coefficient
• Dirichlet boundary value problem for stochastic parabolic equations: compatibility relations and regularity of solutions
• Numerical solution of an inverse medium scattering problem with a stochastic source
• Lipschitz stability in inverse parabolic problems by the Carleman estimate
• Global uniqueness of a multidimensional inverse problem for a nonlinear parabolic equation by a Carleman estimate
• Estimates of initial conditions of parabolic equations and inequalities via lateral Cauchy data
• Inverse source problem for a transmission problem for a parabolic equation

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