Extended-domain-Lavrentiev's regularization for the Cauchy problem

DOI10.1088/0266-5611/27/4/045005zbMath1227.65088OpenAlexW2028936707MaRDI QIDQ2996603

Duc Thang Du, Faker Ben Belgacem, Faten Jelassi

Publication date: 3 May 2011

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

Full work available at URL: https://doi.org/10.1088/0266-5611/27/4/045005

zbMATH Keywords

convergencenumerical examplesLaplace equationLavrentiev regularizationdata completionill-posed Cauchy problem

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (8)

Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems ⋮ A variational-type method of fundamental solutions for a Cauchy problem of Laplace's equation ⋮ Local convergence of the Lavrentiev method for the Cauchy problem via a Carleman inequality ⋮ A Tikhonov regularization method for Cauchy problem based on a new relaxation model ⋮ Solving a nonlinear inverse Robin problem through a linear Cauchy problem ⋮ A regularization method for a Cauchy problem of Laplace's equation in an annular domain ⋮ A coupled complex boundary method for the Cauchy problem ⋮ Data completion method for the Helmholtz equation via surface potentials for partial Cauchy data

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