Solution of the backward problem for the space-time fractional diffusion equation related to the release history of a groundwater contaminant

• Published in: Journal of inverse and ill-posed problems Vol. 32; no. 1; pp. 107 - 126
• Main Authors: Salehi Shayegan, Amir Hossein, Zakeri, Ali, Salehi Shayegan, Adib
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.02.2024; Walter de Gruyter GmbH
• Subjects: 47A52; 65N21; Algorithms; Backward space-time fractional diffusion equation; computational algorithm; conjugate gradient algorithm; Contaminants; Existence theorems; Finite element method; Groundwater; Ill posed problems; Iterative algorithms; Iterative methods; Landweber iteration algorithm; Landweber's iteration algorithm; Lipschitz condition; Mathematical analysis; quasi-solution; Regularization; Uniqueness theorems

Finding the history of a groundwater contaminant plume from final measurements is an ill-posed problem and, consequently, its solution is extremely sensitive to errors in the input data. In this paper, we study this problem mathematically. So, firstly, existence and uniqueness theorems of a quasi-so...