Reconstruction and stable recovery of source terms appearing in diffusion equations

Yavar Kian (1, 2) , Masahiro Yamamoto (3)

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

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary conditions we prove that some class of source terms which are independent of one space direction, can be reconstructed from boundary measurements. Actually , we prove that this inverse problem is well-posed. We establish also some results of Lipschitz stability for the recovery of source terms which we apply to the stable recovery of time-dependent coefficients.

Mots clés: Inverse source problems; well-posedness; reconstruction; stability estimate; fractional diffusion equation

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian, Masahiro Yamamoto. Reconstruction and stable recovery of source terms appearing in diffusion equations. Inverse Problems, 2019, 35 (11), pp.115006. ⟨10.1088/1361-6420/ab2d42⟩. ⟨hal-02049174⟩