Datum predavanja: petak, 5. 2. 2021.
Vrijeme predavanja: 11h
Christian, Monotoya, Unidu
Title: Inverse source problems for coupled heat systems using measurements of one scalar state.
In this talk we present inverse source problems for coupled systems of heat equations with constant or spatial–dependent coupling terms and whose internal measurements involve a reduced number of observed states. The methodology involves null controllability results, Volterra equations and spectral analysis. Briefly speaking, the analysis is developed
for three kind of systems: the first one consists of parabolic equations with zero order coupling terms (or the so–called non–self–adjoint matrix potential) and whose possibly space–dependent coefficients. The second one consists of parabolic equations with coupling in the diffusion matrix. For these kinds of systems we establish source reconstruction formulas using internal measurements of one scalar state.
Numerical examples in 2D are illustrated, showing it that the algorithms make possible to recover space–dependent sources. Finally, we describe a Lipschitz–type stability for the spatial factor in the source term using observation data on an arbitrary fixed sub–domain related to only one scalar state.