The inverse source problem for time-fractional diffusion equation: stability analysis and regularization

DOI10.1080/17415977.2014.968148zbMath1329.35357OpenAlexW2081325304MaRDI QIDQ3466144

Chu-Li Fu, Fan Yang, Xiao-Xiao Li

Publication date: 1 February 2016

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2014.968148

zbMATH Keywords

optimal error bounda posteriori parameter choicetime-fractional diffusion equationtime-dependent heat sourcea conditional stability

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Linear operators and ill-posed problems, regularization (47A52) Fractional partial differential equations (35R11)

Related Items (25)

Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates ⋮ Three Landweber iterative methods for solving the initial value problem of time-fractional diffusion-wave equation on spherically symmetric domain ⋮ Two regularization methods for identifying the source term problem on the time-fractional diffusion equation with a hyper-Bessel operator ⋮ The quasi-boundary value method for identifying the initial value of the space-time fractional diffusion equation ⋮ Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation ⋮ The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation ⋮ Reconstruction of pointwise sources in a time-fractional diffusion equation ⋮ Simultaneous determination of the space-dependent source and initial value for a two-dimensional heat conduction equation ⋮ On the simultaneous reconstruction of the initial diffusion time and source term for the time-fractional diffusion equation ⋮ Landweber iterative method for an inverse source problem of time-space fractional diffusion-wave equation ⋮ Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems ⋮ Numerical solution of time-dependent component with sparse structure of source term for a time fractional diffusion equation ⋮ Landweber iterative regularization method for identifying the unknown source of the time-fractional diffusion equation ⋮ An inverse source problem for a two-parameter anomalous diffusion with local time datum ⋮ Conditional stability for an inverse coefficient problem of a weakly coupled time-fractional diffusion system with half order by Carleman estimate ⋮ Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity ⋮ Optimal regularization for an unknown source of space-fractional diffusion equation ⋮ A quasi-boundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain ⋮ Inverse source in two-parameter anomalous diffusion, numerical algorithms, and simulations over graded time meshes ⋮ A regularization framework for mildly ill-posed problems connected with pseudo-differential operator ⋮ Identifying an unknown source term in a time-space fractional parabolic equation ⋮ Inverse source problem for a distributed-order time fractional diffusion equation ⋮ An iterative method for an inverse source problem of time-fractional diffusion equation ⋮ A numerical method based on the Jacobi polynomials to reconstruct an unknown source term in a time fractional diffusion-wave equation ⋮ A direct parallel-in-time quasi-boundary value method for inverse space-dependent source problems

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