Existence and stability of nonequilibrium steady states of Nernst–Planck–Navier–Stokes systems
Abstract We consider the Nernst–Planck–Navier–Stokes system in a bounded domain of R
d, d= 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic …
d, d= 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic …
[PDF][PDF] On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis
PA Markowich, C Villani - Mat. Contemp, 2000 - cedricvillani.org
We present connections between the problem of trend to equilibrium for the Fokker-Planck
equation of statistical physics, and several inequalities from functional analysis, like …
equation of statistical physics, and several inequalities from functional analysis, like …
On the Nernst–Planck–Navier–Stokes system
P Constantin, M Ignatova - Archive for Rational Mechanics and Analysis, 2019 - Springer
We consider ionic electrodiffusion in fluids, described by the Nernst–Planck–Navier–Stokes
system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the …
system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the …
A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson–Nernst–Planck equations
J Hu, X Huang - Numerische Mathematik, 2020 - Springer
Abstract The Poisson–Nernst–Planck (PNP) equations is a macroscopic model widely used
to describe the dynamics of ion transport in ion channels. In this paper, we introduce a semi …
to describe the dynamics of ion transport in ion channels. In this paper, we introduce a semi …
Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type
M Kurokiba, T Ogawa - 2003 - projecteuclid.org
We discuss the existence of the blow-up solution for some nonlinear parabolic system called
attractive drift-diffusion equation in two space dimensions. We show that if the initial data …
attractive drift-diffusion equation in two space dimensions. We show that if the initial data …
Energetically stable discretizations for charge transport and electrokinetic models
A finite element discretization using a method of lines approached is proposed for
approximately solving the Poisson–Nernst–Planck (PNP) equations. This discretization …
approximately solving the Poisson–Nernst–Planck (PNP) equations. This discretization …
A free energy satisfying finite difference method for Poisson–Nernst–Planck equations
In this work we design and analyze a free energy satisfying finite difference method for
solving Poisson–Nernst–Planck equations in a bounded domain. The algorithm is of second …
solving Poisson–Nernst–Planck equations in a bounded domain. The algorithm is of second …
Poisson–Nernst–Planck systems for narrow tubular-like membrane channels
We study global asymptotic behavior of Poisson–Nernst–Planck (PNP) systems for flow of
two ion species through a narrow tubular-like membrane channel. As the radius of the cross …
two ion species through a narrow tubular-like membrane channel. As the radius of the cross …
Nernst–Planck–Navier–Stokes systems far from equilibrium
We consider ionic electrodiffusion in fluids, described by the Nernst–Planck–Navier–Stokes
system. We prove that the system has global smooth solutions for arbitrary smooth data in …
system. We prove that the system has global smooth solutions for arbitrary smooth data in …
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson–Nernst–Planck systems
We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for
solving time-dependent Poisson–Nernst–Planck systems. Both the semi-discrete and fully …
solving time-dependent Poisson–Nernst–Planck systems. Both the semi-discrete and fully …