A local stability estimate for an inverse heat source problem

Abdelkrim Chakib (1) , Abdeljalil Nachaoui (2) , Ahmed Zeghal (1)

1 Laboratoire de mathématiques et applications
2 LMJL - Laboratoire de Mathématiques Jean Leray

In this paper, we establish some local stability estimate for a problem of determining a domain $D$ appearing in the heat equation: $\frac{\partial u}{\partial t} - \Delta u + \chi_D\,u=0$ from a Neumann additional data on a part of the lateral boundary. This estimate is obtained by taking advantage of some shape optimization tools.

Mots clés: Inverse problem; Heat equation; Local stability estimate; Shape optimization

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Abdelkrim Chakib, Abdeljalil Nachaoui, Ahmed Zeghal. A local stability estimate for an inverse heat source problem. 2006. ⟨hal-00142781⟩