Recovering the initial distribution for space-fractional diffusion equation by a logarithmic regularization method

DOI10.1016/J.AML.2016.06.002zbMath1347.65152OpenAlexW2410949605MaRDI QIDQ308929

Quan-Guo Zhang, Guang-Hui Zheng

Publication date: 6 September 2016

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2016.06.002

zbMATH Keywords

stabilityconvergence ratespace-fractional diffusion equationbackward problemfractional Laplaciana posteriori parameter choicelogarithmic regularization method

Mathematics Subject Classification ID

Heat equation (35K05) Inverse problems for PDEs (35R30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Fractional partial differential equations (35R11)

Related Items (9)

Solving the backward problem in Riesz-Feller fractional diffusion by a new nonlocal regularization method ⋮ On a space fractional backward diffusion problem and its approximation of local solution ⋮ Hölder-logarithmic type approximation for nonlinear backward parabolic equations connected with a pseudo-differential operator ⋮ Stability Results for Backward Nonlinear Diffusion Equations with Temporal Coupling Operator of Local and Nonlocal Type ⋮ On a time-space fractional backward diffusion problem with inexact orders ⋮ Recovering the historical distribution for nonlinear space-fractional diffusion equation with temporally dependent thermal conductivity in higher dimensional space ⋮ Determination of initial distribution for a space-fractional diffusion equation with time-dependent diffusivity ⋮ Solving the Riesz-Feller space-fractional backward diffusion problem by a generalized Tikhonov method ⋮ Fractional filter method for recovering the historical distribution for diffusion equations with coupling operator of local and nonlocal type

Cites Work

• A new \textit{a posteriori} parameter choice strategy for the convolution regularization of the space-fractional backward diffusion problem
• Two regularization methods for solving a Riesz–Feller space-fractional backward diffusion problem
• Fractional Partial Differential Equations and Their Numerical Solutions
• A regularization for a Riesz–Feller space-fractional backward diffusion problem
• A generalized master equation approach to modelling anomalous transport in animal movement
• The fundamental solution of the space-time fractional diffusion equation
• Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation
• An inverse problem for space‐fractional backward diffusion problem

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