Identification of the spatial component in the source term of a space-time fractional diffusion equation

Mohamed Ben Salah (1) , Maatoug Hassine (1)

1 UM - Université de Monastir - University of Monastir

This paper is concerned with an inverse source problem for a space-time fractional diffusion equation. The aim is to reconstruct the spatial component in the source term from partially observed data. The considered ill-posed inverse source problem is formulated as a minimization one. The existence and the stability of the minimization system are discussed. An iterative process is developed for identifying the unknown source term. The efficiency and the accuracy of the algorithm are shown by several numerical experiments.

Mots clés: fractional derivative; inverse source problem; minimization problem; Numerical reconstruction algorithm

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Mohamed Ben Salah, Maatoug Hassine. Identification of the spatial component in the source term of a space-time fractional diffusion equation. CARI 2022, Oct 2022, Monastir, Tunisia. ⟨hal-03752751v2⟩