On generalized Poisson–Nernst–Planck equations with inhomogeneous boundary conditions: a‐priori estimates and stability |
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Authors: | Victor A Kovtunenko Anna V Zubkova |
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Institution: | 1. Institute for Mathematics and Scientific Computing, Karl–Franzens University of Graz, NAWI Graz, Graz, Austria;2. Lavrentyev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, Novosibirsk, Russia |
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Abstract: | In this paper, we consider the strongly nonlinear Nernst–Planck equations coupled with the quasi‐linear Poisson equation under inhomogeneous, moreover, nonlinear boundary conditions. This system describes joint multi‐component electrokinetics in a pore phase. The system is supplemented by the force balance and by the volume and positivity constraints. We establish well‐posedness of the problem in the variational setting. Namely, we prove the existence theorem supported by the energy and the entropy a‐priori estimates, and we provide the Lyapunov stability of the solution as well as its uniqueness in special cases. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | Generalized Poisson– Nernst– Planck model nonlinear parabolic– elliptic system nonlinear boundary conditions existence and uniqueness Lyapunov stability a‐priori estimate |
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