On an inverse problem: recovery of non-smooth solutions to backward heat equation

DOI10.1016/j.apm.2011.11.020zbMath1252.65168OpenAlexW2128897571MaRDI QIDQ693515

Fabien Ternat, Oscar Orellana, Prabir K. Daripa

Publication date: 7 December 2012

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2011.11.020

zbMATH Keywords

heat equationinverse problemnon-smooth solutionsfinite difference methodsillposed problemquasi-reversibility techniques

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items

Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework ⋮ Application of the cut-off projection to solve a backward heat conduction problem in a two-slab composite system ⋮ Fast parallel-in-time quasi-boundary value methods for backward heat conduction problems

Cites Work

• Unnamed Item
• Two stable methods with numerical experiments for solving the backward heat equation
• Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem
• Numerical solution of the equation of heat conduction for preceding times
• An approximate solution of an improper boundary value problem
• Fourier regularization for a backward heat equation
• Short-wave instabilities and ill-posed initial value problems
• A numerical study of an ill-posed Boussinesq equation arising in water and nonlinear lattices: Filtering and regularization techniques
• Some useful filtering techniques for illposed problems
• Entropy- and Tikhonov-based regularization techniques applied to the backwards heat equation
• Solution of inverse diffusion problems by operator-splitting methods
• Group preserving scheme for backward heat conduction problems
• Two numerical methods for solving a backward heat conduction problem
• Global space-time multiquadric method for inverse heat conduction problem
• Existence of Infinitely Many Solutions for a Forward Backward Heat Equation
• Singularity formation during Rayleigh–Taylor instability
• Continuity of Solutions of Parabolic and Elliptic Equations
• A Well Posed Problem for the Backward Heat Equation
• Lattice-free finite difference method for numerical solution of inverse heat conduction problem
• Singular Solutions and Ill-Posedness for the Evolution of Vortex Sheets
• A study of singularity formation in a vortex sheet by the point-vortex approximation
• A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method
• The spontaneous appearance of a singularity in the shape of an evolving vortex sheet
• ASYMPTOTIC BEHAVIOR FOR TWO REGULARIZATIONS OF THE CAUCHY PROBLEM FOR THE BACKWARD HEAT EQUATION
• Optimal Filtering for the Backward Heat Equation
• A regularization of nonlinear diffusion equations in a multiresolution framework