Determination of Time Dependent Factors of Coefficients in Fractional Diffusion Equations

Kenichi Fujishiro (1) , Yavar Kian (2, 3)

1 UTokyo - The University of Tokyo
2 CPT - Centre de Physique Théorique - UMR 7332
3 CPT - E8 Dynamique quantique et analyse spectrale

In the present paper, we consider initial-boundary value problems for partial differential equations with time-fractional derivatives which evolve in Q = Ω × (0, T) where Ω is a bounded domain of R d and T > 0. We study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at a point x 0 ∈ Ω for all t ∈ (0, T).

Domaines: Equations aux dérivées partielles [math.AP]

Kenichi Fujishiro, Yavar Kian. Determination of Time Dependent Factors of Coefficients in Fractional Diffusion Equations. Mathematical Control and Related Fields, 2016, 6 (2), pp.251-269. ⟨10.3934/mcrf.2016003⟩. ⟨hal-01101556v2⟩