A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation
Copyright policy )A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation
We consider a time-fractional diffusion equation for an inverse problem to determine an unknown source term, whereby the input data is obtained at a certain time. In general, the inverse problems are ill-posed in the sense of Hadamard. Therefore, in this study, we propose a mollification regularization method to solve this problem. In the theoretical results, the error estimate between the exact and regularized solutions is given by a priori and a posteriori parameter choice rules. Besides, the proposed regularized methods have been verified by a numerical experiment.
- Ton Duc Thang University Viet Nam
- Macau University of Science and Technology Macao
- Xiangtan University China (People's Republic of)
- Dalat University Viet Nam
- Duy Tan University Viet Nam
Artificial intelligence, Inverse Problems in Mathematical Physics and Imaging, Inverse Scattering Theory, Economics, Inverse Problems, Diffusion equation, Geometry, ill-posed problem, Epistemology, Mathematical analysis, Convergence Analysis of Iterative Methods for Nonlinear Equations, Service (business), QA1-939, FOS: Mathematics, convergence estimates, Regularization (linguistics), Anomalous Diffusion Modeling and Analysis, Mathematical Physics, Hadamard transform, Numerical Analysis, Time-Fractional Diffusion Equation, Mathematical optimization, Economy, A priori and a posteriori, Applied mathematics, Computer science, FOS: Philosophy, ethics and religion, Regularization Methods, Philosophy, Modeling and Simulation, Physical Sciences, Inverse problem, inverse problem, Inverse, time-fractional diffusion equation, Mathematics, Anomalous Diffusion
Artificial intelligence, Inverse Problems in Mathematical Physics and Imaging, Inverse Scattering Theory, Economics, Inverse Problems, Diffusion equation, Geometry, ill-posed problem, Epistemology, Mathematical analysis, Convergence Analysis of Iterative Methods for Nonlinear Equations, Service (business), QA1-939, FOS: Mathematics, convergence estimates, Regularization (linguistics), Anomalous Diffusion Modeling and Analysis, Mathematical Physics, Hadamard transform, Numerical Analysis, Time-Fractional Diffusion Equation, Mathematical optimization, Economy, A priori and a posteriori, Applied mathematics, Computer science, FOS: Philosophy, ethics and religion, Regularization Methods, Philosophy, Modeling and Simulation, Physical Sciences, Inverse problem, inverse problem, Inverse, time-fractional diffusion equation, Mathematics, Anomalous Diffusion
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