Identifiability and stability of an inverse problem involving a Fredholm equation

Carlos Conca (1, 2) , Rodrigo Lecaros (1, 2) , Ortega Jaime (1, 2) , Lionel Rosier (3)

1 CMM - Center for Mathematical Modeling
2 DIM - Departamento de Ingeniería Matemática [Santiago]
3 CAS - Centre Automatique et Systèmes

The authors study a linear inverse problem with a biological interpretation, which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.

Mots clés: Inverse problems; Olfactory system; Kernel determination; Fredholm integral equation; Partial differential equations; Numerical reconstruction

Domaines: Automatique / Robotique

Carlos Conca, Rodrigo Lecaros, Ortega Jaime, Lionel Rosier. Identifiability and stability of an inverse problem involving a Fredholm equation. Chinese Annals of Mathematics - Series B, 2015, 36 (5), pp.737-762. ⟨10.1007/s11401-015-0974-9⟩. ⟨hal-01261672⟩