Existence and uniqueness of a global weak solution of a Darcy-Nernst-Planck-Poisson system

DOI10.1002/gamm.201210013zbMath1261.35121OpenAlexW1970205366MaRDI QIDQ4900446

Peter Knabner, Matthias Herz, Nadja Ray

Publication date: 24 January 2013

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/gamm.201210013

zbMATH Keywords

global existenceMoser iterationfixed point approachelectro-hydrodynamicsDarcy-Nernst-Planck-Poisson system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Weak solutions to PDEs (35D30) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (7)

Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions ⋮ Existence and two-scale convergence of the generalised Poisson–Nernst–Planck problem with non-linear interface conditions ⋮ Mathematical modeling of a discontinuous solution of the generalized Poisson-Nernst-Planck problem in a two-phase medium ⋮ On generalized Poisson-Nernst-Planck equations with inhomogeneous boundary conditions: a-priori estimates and stability ⋮ Homogenization of the generalized Poisson–Nernst–Planck problem in a two-phase medium: correctors and estimates ⋮ Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems ⋮ Global smooth solutions of the Nernst-Planck-Darcy system

Cites Work

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• Incompressible ionized fluid mixtures
• A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
• On Existence, Uniqueness and Asymptotic Behavior of Solutions of the Basic Equations for Carrier Transport in Semiconductors

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