An elliptic problem with strongly nonlinear interface condition. Issue 3 (17th February 2020)

• Record Type: Journal Article
• Authors: Dörfler, Willy; Maier, Markus
• Is Part Of: Applicable analysis. Volume 99:Issue 3(2020)
• Page Start: 479
• Page End: 495
• Publication Date: 2020-02-17
• Subjects: Siegfried Carl; Elliptic boundary value problem -- nonlinear Neumann boundary condition; Primary: 35J65 -- Secondary: 35B51 -- 35J20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1504026
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider a system of partial differential equations arising in the modelling of the electrochemical processes in Li-ion batteries. In this simplification, it consists of two elliptic equations in two domains separated by an interface. At the interface holds a Neumann condition that depends exponentially on the jump of the solution at the interface (Butler–Vollmer equation). We prove unique existence of a solution and a comparison principle.