Partial reconstruction of the source term in a linear parabolic initial problem with first order boundary conditions

Abstract

We consider the inverse problem of identifying a factor in the source term of a parabolic mixed system with first-order boundary conditions. The supplementary information, which is needed to do it, is given by the knowledge of the evolution in time of a certain integral with respect to a suitable Borel measure.

Keywords:

• inverse problems
• parabolic systems
• first-order boundary conditions
• cylindrical domains

AMS Subject Classifications:

• 35K51
• 34K29