Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide

Yavar Kian (1) , Diomba Sambou (2) , Eric Soccorsi (3, 1)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 Facultad de Matemáticas [Santiago de Chile]
3 CPT - Centre de Physique Théorique - UMR 7332

We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with homogeneous initial and Dirichlet data.

Mots clés: Inverse problem; heat equation; time-dependent source term; stability inequality; Carleman estimate; partial boundary data

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian, Diomba Sambou, Eric Soccorsi. Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide. Applicable Analysis, 2020, 99 (13), pp.2210-2228. ⟨10.1080/00036811.2018.1557324⟩. ⟨hal-01428972⟩