A modified Tikhonov regularization method for a backward heat equation

DOI10.1080/17415977.2011.605885zbMath1244.65136OpenAlexW2003211947MaRDI QIDQ2891251

Ze-Hong Meng, Zhen-Yu Zhao

Publication date: 13 June 2012

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2011.605885

zbMATH Keywords

inverse problemnumerical exampleserror estimatediscrepancy principleill-posed problembackward heat equationTikhonov regularization method

Mathematics Subject Classification ID

Heat equation (35K05) Inverse problems for PDEs (35R30) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

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Cites Work

• Fourier regularization for a backward heat equation
• The final value problem for evolution equations
• A mollification method for ill-posed problems
• Solution of inverse diffusion problems by operator-splitting methods
• Optimal error bound and Fourier regularization for identifying an unknown source in the heat equation
• Group preserving scheme for backward heat conduction problems
• A comparison of regularizations for an ill-posed problem
• Optimal Filtering for the Backward Heat Equation
• An iterative boundary element method for solving the one-dimensional backward heat conduction problem

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