Stability result for a time dependent potential in a waveguide

Patricia Gaitan (1) , Yavar Kian (2, 3)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

We consider the operator $H:= \partial_t -\Delta+V$ in $2$D or $3$D waveguide. With an adapted global Carleman estimate with singular weight functions we give a stability result for the time dependent part of the potential for this particular geometry. Two cases are considered: the bounded waveguide with mixed Dirichlet and Neumann conditions and the open waveguide with Dirichlet boundary conditions.

Mots clés: Inverse problems; Carleman estimates; Parabolic equations

Domaines: Equations aux dérivées partielles [math.AP]

Patricia Gaitan, Yavar Kian. Stability result for a time dependent potential in a waveguide. Inverse Problems, 2013, 29. ⟨hal-00677872⟩