Inverse source problem for a distributed-order time fractional diffusion equation

DOI10.1515/jiip-2019-0006OpenAlexW2950409537MaRDI QIDQ2301648

Kewei Liang, Lele Yuan, Xiao-liang Cheng

Publication date: 25 February 2020

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-2019-0006

zbMATH Keywords

convergence analysisTikhonov regularizationMorozov's discrepancy principleinverse source problema-priori parameter choicedistributed-order time fractional diffusion equation

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Inverse problems in optimal control (49N45) Inverse problems for integral equations (45Q05) Fractional partial differential equations (35R11)

Related Items (7)

Blowing-up solutions of distributed fractional differential systems ⋮ Some boundary-value problems of filtration dynamics corresponding to models of fractional diffusion of distributed order ⋮ Identifying a space-dependent source term in distributed order time-fractional diffusion equations ⋮ Solving a backward problem for a distributed-order time fractional diffusion equation by a new adjoint technique ⋮ Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation ⋮ Coupling RBF-based meshless method and Landweber iteration algorithm for approximating a space-dependent source term in a time fractional diffusion equation ⋮ Identification of stationary source in the anomalous diffusion equation

Cites Work

• Unnamed Item
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• Identifying an unknown source in time-fractional diffusion equation by a truncation method
• Weak solutions of fractional differential equations in non cylindrical domains
• An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time
• Regularization methods for large-scale problems
• A mollification regularization method for identifying the time-dependent heat source problem
• Solving an inverse source problem for a time fractional diffusion equation by a modified quasi-boundary value method
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations
• Determination of Robin coefficient in a fractional diffusion problem
• Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations
• Some high-order difference schemes for the distributed-order differential equations
• Two alternating direction implicit difference schemes for two-dimensional distributed-order fractional diffusion equations
• Finite difference/finite element methods for distributed-order time fractional diffusion equations
• Distributed-order fractional diffusions on bounded domains
• A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation
• Distributed order calculus and equations of ultraslow diffusion
• Maximum principle for the generalized time-fractional diffusion equation
• An inverse time-dependent source problem for a time-fractional diffusion equation
• Theory and simulation of time-fractional fluid diffusion in porous media
• Fractional diffusion: recovering the distributed fractional derivative from overposed data
• Inverse source problem for a fractional diffusion equation
• The inverse source problem for time-fractional diffusion equation: stability analysis and regularization
• Structural identification of an unknown source term in a heat equation
• Estimates for a general fractional relaxation equation and application to an inverse source problem
• A tutorial on inverse problems for anomalous diffusion processes
• Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations
• Determination of an Unknown Heat Source from Overspecified Boundary Data
• Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation

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