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Two regularization methods to identify a space-dependent source for the time-fractional diffusion equation. (English) Zbl 1266.65161
Authors’ abstract: The inverse problem of identifying a space-dependent source for the time-fractional diffusion equation is investigated. Such a problem is obtained from the classical diffusion equation in which the time derivative is replaced with a Caputo derivative of order α(0,1]. We show that such a problem is ill-posed and apply the Tikhonov regularization method and a simplified Tikhonov regularization method to solve it based on the solution given by the separation of variables. Convergence estimates are presented under an a priori parameter choice rule and an a posteriori parameter choice rule, respectively. Finally, numerical examples are given to show that the regularization methods are effective and stable.
MSC:
65M32Inverse problems (IVP of PDE, numerical methods)
35R11Fractional partial differential equations
35R30Inverse problems for PDE
35K05Heat equation
65M12Stability and convergence of numerical methods (IVP of PDE)
35R25Improperly posed problems for PDE
65M30Improperly posed problems (IVP of PDE, numerical methods)