Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

Oleg Imanuvilov , Yavar Kian (1, 2) , Masahiro Yamamoto

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

Abstract For a parabolic equation in the spatial variable x = ( x 1 , … , x n ) {x=(x_{1},\ldots,x_{n})} and time t , we consider an inverse problem of determining a coefficient which is independent of one spatial component x n {x_{n}} by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.

Domaines: Equations aux dérivées partielles [math.AP]

Oleg Imanuvilov, Yavar Kian, Masahiro Yamamoto. Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate. Journal of Inverse and Ill-posed Problems, In press, 30 (2), pp.191-203. ⟨10.1515/jiip-2020-0089⟩. ⟨hal-03381623⟩