AN INVERSE SOURCE PROBLEM FOR THE DIFFUSION EQUATION WITH FINAL OBSERVATION

M Bellassoued (1) , M Cristofol (2, 3, 4, 5)

1 UTM - Université de Tunis El Manar
2 I2M - Institut de Mathématiques de Marseille
3 AMU - Aix Marseille Université
4 CNRS - Centre National de la Recherche Scientifique
5 ECM - École Centrale de Marseille

We investigate the inverse problem involving recovery of source temperature from the information of final temperature profile. We prove that we can uniquely recover the source of a n-dimensional heat equation from the measurement of the temperature at fixed time provided that the source is known in an arbitrary subdomain. The algorithm is based on the Carleman estimate. By using a Bukhgeim-Klibanov method, as a first step, we determine the source term by two measurements. A compacity and analyticity arguments procedure help to reduce the number of measurements.

Mots clés: Inverse source problem; parabolic equation; Carleman estimates; Final overdetermination

Domaines: Equations aux dérivées partielles [math.AP]

M Bellassoued, M Cristofol. AN INVERSE SOURCE PROBLEM FOR THE DIFFUSION EQUATION WITH FINAL OBSERVATION. 2016. ⟨hal-01278412⟩