Reaction-diffusion systems in annular domains: source stability estimates with boundary observations

Abstract

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 Lipschitz 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. The main tools are represented by: appropriate Carleman estimates in L^2 norms, with boundary observations, and positivity improving properties for the solutions to parabolic equations and systems.