A new regularized method for two dimensional nonhomogeneous backward heat problem

DOI10.1016/j.amc.2009.06.020zbMath1180.65119OpenAlexW2017156202MaRDI QIDQ734834

Nguyen Huy Tuan, Dang Duc Trong

Publication date: 14 October 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.06.020

zbMATH Keywords

stabilityconvergenceinverse problemnumerical experimentregularization methodill-posed problembackward heat equationFourier sine expansion

Mathematics Subject Classification ID

Heat equation (35K05) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

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Cites Work

• A modified quasi-boundary value method for ill-posed problems
• The final value problem for evolution equations
• \(C\)-semigroups and the Cauchy problem
• Regularization for ill-posed Cauchy problems associated with generators of analytic semigroups
• Regularized semigroups, existence families and the abstract Cauchy problem
• A nonlinear case of the 1-D backward heat problem: regularization and error estimate
• Structural stability for ill-posed problems in Banach space
• Zur Regularisierung einer Klasse nichtkorrekter Probleme bei Evolutionsgleichungen. (On the regularization of a certain class of improperly posed problems for evolution equations)
• Continuous dependence on data for solutions of partial differential equations with a prescribed bound
• The Approximation of Certain Parabolic Equations Backward in Time by Sobolev Equations
• Entire regularizations of strongly continuous groups and products of analytic generators
• Properties of solutions of ordinary differential equations in banach space
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