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Article Dans Une Revue Inverse Problems Année : 2023

Solving time-fractional diffusion equations with a singular source term

Résumé

Abstract This article deals with linear time-fractional diffusion equations with time-dependent singular source term. Whether the order of the time-fractional derivative is multi-term, distributed or space-dependent, we prove that the system admits a unique weak solution enjoying a Duhamel representation, provided that the time-dependence of the source term is a distribution. As an application, the square integrable space-dependent part and the distributional time-dependent part of the source term of a multi-term time-fractional diffusion equation are simultaneously recovered by partial internal observation of the solution.

Dates et versions

hal-04396884 , version 1 (16-01-2024)

Identifiants

Citer

Yavar Kian, Éric Soccorsi. Solving time-fractional diffusion equations with a singular source term. Inverse Problems, 2023, 39 (12), pp.125005. ⟨10.1088/1361-6420/ad0176⟩. ⟨hal-04396884⟩
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