Identifying a space-dependent source term in distributed order time-fractional diffusion equations
Dinh Nguyen Duy Hai
Abstract
The aim of this paper is to investigate an inverse problem of recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such a problem is ill-posed and has important practical applications. For this problem, we propose a general regularization method based on the idea of the filter method. With a suitable source condition, we prove that the method is of optimal order under various choices of regularization parameter. One is based on the a priori regularization parameter choice rule and another one is the discrepancy principle. Finally, the capabilities of our method are illustrated by both the Tikhonov and the Landweber method.
Topics & Concepts
Tikhonov regularizationRegularization (linguistics)A priori and a posterioriTerm (time)Hilbert spaceInverse problemApplied mathematicsMathematicsBackus–Gilbert methodWell-posed problemMathematical optimizationRegularization perspectives on support vector machinesComputer scienceMathematical analysisPhysicsEpistemologyArtificial intelligenceQuantum mechanicsPhilosophyFractional Differential Equations SolutionsNumerical methods in inverse problemsDifferential Equations and Numerical Methods