Fellner Klemens, Kovtunenko Victor A
Institute of Mathematics and Scientific Computing, University of Graz, NAWI Graz, 8010Graz, Austria.
Lavrent'ev Institute of Hydrodynamics, 630090Novosibirsk, Russia.
Appl Anal. 2015 Nov 4;95(12):2661-2682. doi: 10.1080/00036811.2015.1105962. eCollection 2016.
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.
研究了在两种材料界面处具有非齐次罗宾型边界条件的非线性泊松-玻尔兹曼方程。该模型描述了在具有稀固体颗粒的周期性多相介质中由离子浓度矢量产生的静电势。关键问题源于界面跳跃，这使得该问题需要不连续解。基于变分技术，我们推导了不连续问题的均匀化，并建立了直至一阶修正的严格残差误差估计。
