https://tu-dortmund.zoom.us/j/94812627974?pwd=K0ozelQrT3FpTGFQWXJ0blJBVktGUT09

In this talk, we will consider inverse problems for parabolic systems with dynamic boundary conditions. Our main aim is to prove stability estimates for the determination of some unknown parameters appearing in the system, namely, source terms, potentials and initial data, from internal measurements. First, we prove a Lipschitz stability result for a class of source terms by establishing a suitable Carleman estimate. Then we study a nonlinear inverse problem involving the recovery of two radiative potentials simultaneously with initial temperatures. We prove a Lipschitz stability estimate for the potentials using Carleman estimates along with some positivity results of the solutions. Then we infer a logarithmic stability result for the initial temperatures by a logarithmic convexity method. Afterwards, we prove a general logarithmic stability result for initial data in an abstract parabolic system. To do so, we use a general logarithmic convexity result. As an application, we consider the Ornstein-Uhlenbeck equation. Then, we will study the identification of source terms from the final overdetermination in the heat equation with dynamic boundary conditions. For this purpose, we combine a weak solution approach and a gradient method with an adjoint problem. We perform some numerical simulations for the reconstruction of an unknown source term in the 1-D equation. Finally, some conclusions and possible extensions will be mentioned.

Salah-Eddine Chorfi

Cadi Ayyad University, Marrakesh