Simultaneous determination of coefficients, internal sources and an obstacle of a diffusion equation from a single measurement

Yavar Kian (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E8 Dynamique quantique et analyse spectrale

This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single boundary measurement. Namely, we consider the simultaneous unique determination of several class of coefficients, some internal sources (a source term and an initial condition) and an obstacle appearing in a diffusion equation from a single boundary measurement. Our problem can be formulated as the simultaneous determination of information about a diffusion process (velocity field, density of the medium), an obstacle and of the source of diffusion. We consider this problems in the context of a classical diffusion process described by a convection-diffusion equation as well as an anomalous diffusion phenomena described by a time fractional diffusion equation.

Mots clés: Inverse problems; diffusion equation; inverse coefficient problem; inverse source prob- lem; inverse obstacle problem; uniqueness; partial data Mathematics subject classification 2010 : 35R30; 35R11

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian. Simultaneous determination of coefficients, internal sources and an obstacle of a diffusion equation from a single measurement. Inverse Problems, 2022, 38 (7), pp.075008. ⟨10.1088/1361-6420/ac70f1⟩. ⟨hal-03001357⟩