A new version of quasi-boundary value method for a 1-D nonlinear ill-posed heat problem

DOI10.1515/JIIP.2009.053zbMath1184.35311OpenAlexW1999057451MaRDI QIDQ5187992

Nguyen Huy Tuan, Pham Hoang Quan, Dang Duc Trong

Publication date: 10 March 2010

Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2009.053

zbMATH Keywords

contraction principlebackward heat problemquasi-boundary value methodsnonlinearly ill-posed problemquasi-reversibility methods

Mathematics Subject Classification ID

Heat equation (35K05) Ill-posed problems for PDEs (35R25) Applications of operator theory to differential and integral equations (47N20) Nonlinear ill-posed problems (47J06) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (5)

On an asymmetric backward heat problem with the space and time-dependent heat source on a disk ⋮ Analysis and numerical simulation of the three-dimensional Cauchy problem for quasi-linear elliptic equations ⋮ An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition ⋮ Numerical methods for the forward and backward problems of a time-space fractional diffusion equation ⋮ A two-dimensional backward heat problem with statistical discrete data

Cites Work

• A modified quasi-boundary value method for ill-posed problems
• The final value problem for evolution equations
• Continuous dependence on modeling for some well-posed perturbations of the backward heat equation
• Structural stability for ill-posed problems in Banach space
• Unique continuation for parabolic differential equations and inequalities
• Approximation of a parabolic non-linear evolution equation backwards in time
• Regularization for a class of ill-posed Cauchy problems
• A nonlinearly backward heat problem: uniqueness, regularization and error estimate

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