Speaker
Description
We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions, in domains with a particular geometry (annular type domains). We establish specific Carleman estimates with boundary observations relying on the possibility of choosing special auxiliary functions, due to the geometry of the domain. These observability estimates are useful in approaching controllability and stabilization problems associated to such systems, as well as for source stability estimates. We establish stability estimates in $L^2$ norm for the source in terms of the solution and/or its normal derivative on a connected component of the boundary. Another important ingredient here is represented by the positivity improving properties for the flow asssociated to parabolic systems. By carefully analyzing the Carleman estimates with internal observations, we also obtain an unique continuation result at initial type for systems of parabolic equations.