Regularization of backward time-fractional parabolic equations by Sobolev-type equations

DOI10.1515/jiip-2020-0062zbMath1461.35228arXiv2004.07349OpenAlexW3092577605MaRDI QIDQ2660777

Nguyen Van Thang, Nguyen Van Duc, Dinh Nho Hào, Nguyen Trung Thành

Publication date: 31 March 2021

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

Full work available at URL: https://arxiv.org/abs/2004.07349

zbMATH Keywords

numerical implementationSobolev-type equationsbackward time-fractional parabolic equations

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Fractional partial differential equations (35R11)

Related Items (6)

Source identification problems for abstract semilinear nonlocal differential equations ⋮ A Source Identification Problem in a Bi-parabolic Equation: Convergence Rates and Some Optimal Results ⋮ A regularization method for Caputo fractional derivatives in the Banach space \(L^\infty [0, T\)] ⋮ On backward fractional pseudo parabolic equation: regularization by quasi-boundary value method, convergence rates ⋮ Identifying an unknown source term in a time-space fractional parabolic equation ⋮ The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Data regularization for a backward time-fractional diffusion problem
• Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• The final value problem for evolution equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Tikhonov regularization method for a backward problem for the time-fractional diffusion equation
• Solving a final value fractional diffusion problem by boundary condition regularization
• A posteriori regularization parameter choice rule for the quasi-boundary value method for the backward time-fractional diffusion problem
• Zur Regularisierung einer Klasse nichtkorrekter Probleme bei Evolutionsgleichungen. (On the regularization of a certain class of improperly posed problems for evolution equations)
• A modified quasi-boundary value method for the backward time-fractional diffusion problem
• The Approximation of Certain Parabolic Equations Backward in Time by Sobolev Equations
• Approximation of a parabolic non-linear evolution equation backwards in time
• Sobolev regularization of a nonlinear ill-posed parabolic problem as a model for aggregating populations
• Faedo-Galerkin approximate solutions for nonlocal fractional differential equation of Sobolev type
• Note on a regularization of a parabolic nonlinear evolution equation backwards in time
• An Introduction to Partial Differential Equations
• Stability results for backward time-fractional parabolic equations
• A tutorial on inverse problems for anomalous diffusion processes
• Fourier regularization for a final value time-fractional diffusion problem
• Total variation regularization for a backward time-fractional diffusion problem
• Regularization for a class of ill-posed Cauchy problems
• A backward problem for the time‐fractional diffusion equation
• A backward problem for the time-fractional diffusion equation

This page was built for publication: Regularization of backward time-fractional parabolic equations by Sobolev-type equations