Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method

DOI10.1080/17415977.2021.1900841OpenAlexW3136086822MaRDI QIDQ5036797

Fan Yang, Qianchao Wang, Xiao-Xiao Li

Publication date: 23 February 2022

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

Full work available at URL: https://doi.org/10.1080/17415977.2021.1900841

zbMATH Keywords

inverse problemoptimal error boundspace-time fractional diffusion equationCaputo-Fabrizio fractional derivativeunknown source identification

Mathematics Subject Classification ID

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

Related Items (3)

The quasi-reversibility regularization method for backward problem of the multi-term time-space fractional diffusion equation ⋮ Two regularization methods for identifying the unknown source in a multiterm time-fractional diffusion equation ⋮ Three regularization methods for identifying the initial value of time fractional advection-dispersion equation

Cites Work

• Unnamed Item
• Unnamed Item
• Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation
• A modified Tikhonov regularization method for the Cauchy problem of Laplace equation
• Fourier regularization method of a sideways heat equation for determining surface heat flux
• On the optimality of methods for ill-posed problems
• On optimal regularization methods for fractional differentiation
• On the optimality of regularization methods for solving linear ill-posed problems
• Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation
• Optimal error bound and modified kernel method for a space-fractional backward diffusion problem
• A second order Crank-Nicolson scheme for fractional Cattaneo equation based on new fractional derivative
• Tikhonov regularization method for a backward problem for the time-fractional diffusion equation
• A modified kernel method for a time-fractional inverse diffusion problem
• A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation
• A quasi-boundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain
• Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain
• A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative
• Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative
• 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
• The quasi-boundary value method for identifying the initial value of heat equation on a columnar symmetric domain
• A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative
• The quasi-reversibility regularization method for identifying the unknown source for time fractional diffusion equation
• Landweber iterative regularization method for identifying the unknown source of the modified Helmholtz equation
• Optimal stable solution of Cauchy problems for elliptic equations
• An \textit{a posteriori} Fourier regularization method for identifying the unknown source of the space-fractional diffusion equation
• A posteriori regularization parameter choice rule for a modified kernel method for a time-fractional inverse diffusion problem
• A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation
• A mollification regularization method for unknown source in time-fractional diffusion equation
• A quasi-reversibility regularization method for the Cauchy problem of the Helmholtz equation
• Landweber iteration regularization method for identifying unknown source on a columnar symmetric domain
• Optimal stable approximations for the sideways heat equation
• Optimality for ill-posed problems under general source conditions
• Regularization of exponentially ill-posed problems
• The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation
• A potential-free field inverse Schrödinger problem: optimal error bound analysis and regularization method
• A modified kernel method for numerical analytic continuation
• Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method

This page was built for publication: Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method