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

TL;DR

This paper develops Lipschitz stability estimates for reaction-diffusion systems in annular domains, linking source stability to boundary observations using Carleman estimates and positivity properties.

Contribution

It introduces new stability estimates for coupled reaction-diffusion systems in annular geometries based on boundary data, expanding inverse problem techniques.

Findings

Lipschitz stability estimates in L^2 norm for sources

Use of Carleman estimates with boundary observations

Positivity properties for parabolic systems

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.