Reconstructing the past from imprecise knowledge of the present: Effective non‐uniqueness in solving parabolic equations backward in time

DOI10.1002/mma.2582zbMath1302.65213OpenAlexW2013388173MaRDI QIDQ4908130

Alfred S. Carasso

Publication date: 4 March 2013

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2582

zbMATH Keywords

non-uniquenessbackward parabolic equationsimage deblurringadvection dispersion equationVan Cittert iterationill-posed continuationhydrologic inversion

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Continuation and prolongation of solutions to PDEs (35B60) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Second-order parabolic equations (35K10) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (13)

Continuous dependence and convergence for a Kelvin-Voigt fluid of order one ⋮ Stabilization estimates for the Brinkman-Forchheimer-Kelvin-Voigt equation backward in time ⋮ Analysis of a Quasi-Reversibility Method for a Terminal Value Quasi-Linear Parabolic Problem with Measurements ⋮ Stabilized Richardson leapfrog scheme in explicit stepwise computation of forward or backward nonlinear parabolic equations ⋮ Compensating operators and stable backward in time marching in nonlinear parabolic equations ⋮ Stability in Kelvin-Voigt poroelasticity ⋮ Stable explicit time marching in well-posed or ill-posed nonlinear parabolic equations ⋮ Stable explicit stepwise marching scheme in ill-posed time-reversed viscous wave equations ⋮ Stabilized backward in time explicit marching schemes in the numerical computation of ill-posed time-reversed hyperbolic/parabolic systems ⋮ Stable explicit stepwise marching scheme in ill-posed time-reversed 2D Burgers' equation ⋮ Computing ill-posed time-reversed 2D Navier–Stokes equations, using a stabilized explicit finite difference scheme marching backward in time ⋮ Stabilized leapfrog scheme run backward in time, and the explicit O(Δ t)² stepwise computation of ill-posed time-reversed 2D Navier–Stokes equations ⋮ Data assimilation in 2D viscous Burgers equation using a stabilized explicit finite difference scheme run backward in time

Uses Software

• PDECHEB

Cites Work

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