Reaction-diffusion systems in annular domains: source stability estimates with boundary observations
Analysis of PDEs
2024-07-02 v1
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.
Cite
@article{arxiv.2407.00399,
title = {Reaction-diffusion systems in annular domains: source stability estimates with boundary observations},
author = {Catalin-George Lefter and Elena-Alexandra Melnig},
journal= {arXiv preprint arXiv:2407.00399},
year = {2024}
}