Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system
Abstract
We establish the well-posedness of a coupled micro-macro parabolic-elliptic system modeling the interplay between two pressures in a gas-liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro-macro Robin problem, potentially useful in identifying quantitatively a micro-macro interfacial Robin transfer coefficient given microscopic measurements on accessible fixed interfaces. To tackle the solvability issue we use two-scale energy estimates and two-scale regularity/compactness arguments cast in the Schauder's fixed point theorem. A number of auxiliary problems, regularity, and scaling arguments are used in ensuring the suitable Fr\'echet differentiability of the solution and the structure of the inverse stability estimate.
Keywords
Cite
@article{arxiv.1701.09122,
title = {Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system},
author = {Martin Lind and Adrian Muntean and Omar Richardson},
journal= {arXiv preprint arXiv:1701.09122},
year = {2018}
}