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The Generalized Poisson–Nernst–Planck System with Nonlinear Interface Conditions

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Book cover Extended Abstracts Summer 2016

Part of the book series: Trends in Mathematics ((RPCRMB,volume 10))

Abstract

We investigate a generalization of the nonlinear Poisson–Nernst–Planck system with respect to coupling phenomena, volume balance and positivity of species concentrations, and nonlinear interface conditions. We aim at existence, uniqueness and the Lyapunov stability of the solution. This system is motivated by applications to modeling of electro-kinetic phenomena in bio- and electro-chemistry.

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Author information

Authors and Affiliations

  1. Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz, NAWI Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Anna V. Zubkova

Authors
  1. Anna V. Zubkova
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Correspondence to Anna V. Zubkova .

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Editors and Affiliations

  1. Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

    Andrei Korobeinikov

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Zubkova, A.V. (2018). The Generalized Poisson–Nernst–Planck System with Nonlinear Interface Conditions. In: Korobeinikov, A. (eds) Extended Abstracts Summer 2016. Trends in Mathematics(), vol 10. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01153-6_18

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