ITERATED QUASI-REVERSIBILITY METHOD APPLIED TO ELLIPTIC AND PARABOLIC DATA COMPLETION PROBLEMS

Jérémi Dardé (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We demonstrate the convergence of the regularized solution to the exact one, and propose a strategy to deal with noise on the data. We present numerical experiments for both problems: a two-dimensional corrosion detection problem and the one-dimensional heat equation with lateral data. In both cases, the method prove to be efficient even with highly corrupted data.

Mots clés: Ill-Posed Inverse Problems; Quasi-reversibility method

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

Jérémi Dardé. ITERATED QUASI-REVERSIBILITY METHOD APPLIED TO ELLIPTIC AND PARABOLIC DATA COMPLETION PROBLEMS. Inverse Problems and Imaging , 2016, 10, ⟨10.3934/ipi.2016005⟩. ⟨hal-01136395⟩