Stable reconstruction of the initial condition in parabolic equations from boundary observations

DOI10.1016/j.camwa.2020.02.019zbMath1446.65096OpenAlexW3010829958MaRDI QIDQ2192532

Bandar Bin-Mohsin, Phan Xuan Thanh, Dinh Nho Hào, Nguyen Huu Cong

Publication date: 17 August 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2020.02.019

zbMATH Keywords

parabolic equationsleast squares methodboundary observationenergy space methodJ.-L. Lions' methodreconstruction of the initial condition

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Boundary element methods for boundary value problems involving PDEs (65N38) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Second-order parabolic equations (35K10) Boundary element methods for initial value and initial-boundary value problems involving PDEs (65M38) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (1)

Determination of the initial density in nonlocal diffusion from final time measurements

Cites Work

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• Determination of the initial condition in parabolic equations from boundary observations
• Determination of a term in the right-hand side of parabolic equations
• Boundary integral operators for the heat equation
• Estimates of initial conditions of parabolic equations and inequalities in infinite domains via lateral Cauchy data
• Stabilization of ill-posed Cauchy problems for parabolic equations
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Carleman estimates for the regularization of ill-posed Cauchy problems
• Conditional stability and numerical reconstruction of initial temperature
• Control operators and iterative algorithms in variational data assimilation problems
• Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems
• Stability results for backward parabolic equations with time-dependent coefficients
• Unicité du prolongement des solutions pour quelques opérateurs différentiels paraboliques
• Carleman estimates for parabolic equations and applications
• A noncharacteristic cauchy problem for linear parabolic equations II: a variational method
• A noncharacteristic cauchy problem for linear parabolic equations III: a variational method and its approximation schemes
• A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$
• A boundary element method for a multi-dimensional inverse heat conduction problem
• Estimates of initial conditions of parabolic equations and inequalities via lateral Cauchy data
• Determination of the initial condition in parabolic equations from integral observations
• Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates
• Inverse problems for partial differential equations

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