A discontinuous Poisson–Boltzmann equation with interfacial jump: homogenisation and residual error estimate. Issue 12 (1st December 2016)

• Record Type: Journal Article
• Authors: Fellner, Klemens; Kovtunenko, Victor A.
• Is Part Of: Applicable analysis. Volume 95:Issue 12(2016)
• Page Start: 2661
• Page End: 2682
• Publication Date: 2016-12-01
• Subjects: Electro-kinetic -- steady-state Poisson–Nernst–Planck system -- Boltzmann statistics -- nonlinear Poisson equation -- Robin condition -- interfacial jump -- oscillating coefficients -- homogenisation -- error corrector; 35B27 -- 35J60 -- 78A57 -- 82B24; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1105962
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : A nonlinear Poisson–Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.