Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Lind, M.; Muntean, A.; Richardson, O. M.
• Is Part Of: Applicable analysis. Volume 97:Issue 1(2018)
• Page Start: 89
• Page End: 106
• Publication Date: 2018-01-02
• Subjects: Upscaled porous media -- two-scale PDE -- inverse micro–macro Robin problem; 76S05 -- 35B27 -- 35R10 -- 35R30 -- 86A22; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1364366
• Languages: English
• ISSNs: 0003-6811

Abstract

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 Fréchet differentiability of the solution and the structure of the inverse stability estimate.