Journal of Computational Physics, ISSN 0021-9991, 10/2014, Volume 274, pp. 633 - 653

In this paper we present a novel hybrid finite-difference/finite-volume method for the numerical solution of the nonlinear Poisson–Nernst–Planck (PNP)...

Level-set | Nonlinear Poisson–Nernst–Planck equation | Second-order discretization | Non-graded adaptive grid | Quadtree data structure | Supercapacitors | Arbitrary geometries | Nonlinear Poisson-Nernst-Planck equation | ELECTROCHEMICAL SYSTEMS | GRAMICIDIN | SIMULATION | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE SCHEME | BOUNDARY MIB METHOD | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CHANNEL | IRREGULAR DOMAINS | DIFFUSE DOUBLE-LAYER | MATCHED INTERFACE | Computer science | Algorithms | Capacitors | Mechanical engineering | Nonlinear dynamics | Discretization | Mathematical analysis | Data structures | Nonlinearity | Mathematical models | Three dimensional

Level-set | Nonlinear Poisson–Nernst–Planck equation | Second-order discretization | Non-graded adaptive grid | Quadtree data structure | Supercapacitors | Arbitrary geometries | Nonlinear Poisson-Nernst-Planck equation | ELECTROCHEMICAL SYSTEMS | GRAMICIDIN | SIMULATION | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE SCHEME | BOUNDARY MIB METHOD | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CHANNEL | IRREGULAR DOMAINS | DIFFUSE DOUBLE-LAYER | MATCHED INTERFACE | Computer science | Algorithms | Capacitors | Mechanical engineering | Nonlinear dynamics | Discretization | Mathematical analysis | Data structures | Nonlinearity | Mathematical models | Three dimensional

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 11/2018, Volume 77, Issue 2, pp. 793 - 817

In this paper, a linearized local conservative mixed finite element method is proposed and analyzed for Poisson–Nernst–Planck (PNP) equations, where the mass...

Computational Mathematics and Numerical Analysis | 65N12 | 35K61 | Theoretical, Mathematical and Computational Physics | Unconditional convergence | Mathematics | Raviart–Thomas element | Mixed finite element method | Algorithms | Mathematical and Computational Engineering | Poisson–Nernst–Planck equations | Optimal error estimate | Conservative schemes | 65N30 | SYSTEM | MATHEMATICS, APPLIED | Poisson-Nernst-Planck equations | RaviartThomas element | RECOVERY | DISCRETIZATION | TRANSPORT | ERROR ANALYSIS | CONVERGENCE | TIME BEHAVIOR | Finite element method | Analysis | Methods

Computational Mathematics and Numerical Analysis | 65N12 | 35K61 | Theoretical, Mathematical and Computational Physics | Unconditional convergence | Mathematics | Raviart–Thomas element | Mixed finite element method | Algorithms | Mathematical and Computational Engineering | Poisson–Nernst–Planck equations | Optimal error estimate | Conservative schemes | 65N30 | SYSTEM | MATHEMATICS, APPLIED | Poisson-Nernst-Planck equations | RaviartThomas element | RECOVERY | DISCRETIZATION | TRANSPORT | ERROR ANALYSIS | CONVERGENCE | TIME BEHAVIOR | Finite element method | Analysis | Methods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 19, pp. 6979 - 6994

In this paper we developed accurate finite element methods for solving 3-D Poisson–Nernst–Planck (PNP) equations with singular permanent charges for simulating...

Molecular surface | Poisson–Nernst–Planck equations | Electrodiffusion | Conditioning | Boundary condition | Finite element | Singular charges | Poisson-Nernst-Planck equations | NUMERICAL-METHODS | APPROXIMATION | ION-TRANSPORT | MODEL | BOLTZMANN EQUATION | PHYSICS, MATHEMATICAL | MOLECULES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ACETYLCHOLINESTERASE | PARTIAL-DIFFERENTIAL-EQUATIONS | SYSTEMS | ELECTROSTATICS | Finite element method | Solvents | Computer simulation | Mathematical analysis | Biomolecules | Mathematical models | Electrostatics | DIFFERENTIAL EQUATIONS | NUMERICAL SOLUTION | APPROXIMATIONS | CALCULATION METHODS | EQUATIONS | POISSON EQUATION | FINITE ELEMENT METHOD | BOUNDARY CONDITIONS | MATHEMATICAL SOLUTIONS | NONLINEAR PROBLEMS | PARTIAL DIFFERENTIAL EQUATIONS | CHARGED PARTICLES | MATRICES | NEWTON METHOD | ITERATIVE METHODS | MATHEMATICAL METHODS AND COMPUTING

Molecular surface | Poisson–Nernst–Planck equations | Electrodiffusion | Conditioning | Boundary condition | Finite element | Singular charges | Poisson-Nernst-Planck equations | NUMERICAL-METHODS | APPROXIMATION | ION-TRANSPORT | MODEL | BOLTZMANN EQUATION | PHYSICS, MATHEMATICAL | MOLECULES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ACETYLCHOLINESTERASE | PARTIAL-DIFFERENTIAL-EQUATIONS | SYSTEMS | ELECTROSTATICS | Finite element method | Solvents | Computer simulation | Mathematical analysis | Biomolecules | Mathematical models | Electrostatics | DIFFERENTIAL EQUATIONS | NUMERICAL SOLUTION | APPROXIMATIONS | CALCULATION METHODS | EQUATIONS | POISSON EQUATION | FINITE ELEMENT METHOD | BOUNDARY CONDITIONS | MATHEMATICAL SOLUTIONS | NONLINEAR PROBLEMS | PARTIAL DIFFERENTIAL EQUATIONS | CHARGED PARTICLES | MATRICES | NEWTON METHOD | ITERATIVE METHODS | MATHEMATICAL METHODS AND COMPUTING

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2017, Volume 40, Issue 6, pp. 2284 - 2299

In this paper, we consider the strongly nonlinear Nernst–Planck equations coupled with the quasi‐linear Poisson equation under inhomogeneous, moreover,...

Generalized Poisson–Nernst–Planck model | Lyapunov stability | a‐priori estimate | nonlinear parabolic–elliptic system | existence and uniqueness | nonlinear boundary conditions | Nonlinear boundary conditions | Nonlinear parabolic–elliptic system | A-priori estimate | Existence and uniqueness | a-priori estimate | MATHEMATICS, APPLIED | FLUID | Generalized Poisson-Nernst-Planck model | nonlinear parabolic-elliptic system | Stability | Mathematical analysis | Electrokinetics | Poisson equation | Nonlinearity | Boundary conditions | Entropy | Estimates

Generalized Poisson–Nernst–Planck model | Lyapunov stability | a‐priori estimate | nonlinear parabolic–elliptic system | existence and uniqueness | nonlinear boundary conditions | Nonlinear boundary conditions | Nonlinear parabolic–elliptic system | A-priori estimate | Existence and uniqueness | a-priori estimate | MATHEMATICS, APPLIED | FLUID | Generalized Poisson-Nernst-Planck model | nonlinear parabolic-elliptic system | Stability | Mathematical analysis | Electrokinetics | Poisson equation | Nonlinearity | Boundary conditions | Entropy | Estimates

Journal Article

Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 05/2019, Volume 35, Issue 3, pp. 1206 - 1223

This article concerns with the superconvergence analysis of bilinear finite element method (FEM) for nonlinear Poisson–Nernst–Planck (PNP) equations. By...

bilinear element | superclose and superconvergence estimates | semi‐discrete and fully‐discrete schemes | semi-discrete and fully-discrete schemes | MATHEMATICS, APPLIED | DEPENDENT MAXWELLS EQUATIONS | Finite element method | Analysis | Methods | Interpolation | Finite element analysis | Nonlinear programming | Mathematical analysis

bilinear element | superclose and superconvergence estimates | semi‐discrete and fully‐discrete schemes | semi-discrete and fully-discrete schemes | MATHEMATICS, APPLIED | DEPENDENT MAXWELLS EQUATIONS | Finite element method | Analysis | Methods | Interpolation | Finite element analysis | Nonlinear programming | Mathematical analysis

Journal Article

Transport in Porous Media, ISSN 0169-3913, 11/2010, Volume 85, Issue 2, pp. 565 - 592

A numerical scheme for the transient solution of a generalized version of the Poisson–Nernst–Planck (PNP) equations is presented. The finite element method is...

Geotechnical Engineering | Porous media | Gauss’ law | Earth Sciences | Hydrogeology | Nernst–Planck equations | Civil Engineering | Mixture theory | Industrial Chemistry/Chemical Engineering | Diffusion | Classical Continuum Physics | Nernst-Planck equations | Gauss'law | ENGINEERING, CHEMICAL | MULTICOMPONENT | TRANSPORT | SWELLING POROUS-MEDIA | MULTIPHASE THERMODYNAMICS | Gauss' law | FORMULATION | ELECTROQUASISTATICS | Finite element method | Surface charge | Nonlinear equations | Constitutive relationships | Deformation | Legislation | Porous materials | Velocity distribution | Matrix methods | Ion diffusion | Constituents | Mathematical analysis | Lagrange multipliers | Constitutive equations | Law | Mathematical models | Entropy | Samhällsbyggnadsteknik | Teknik och teknologier | Engineering and Technology | Construction Management | Byggproduktion

Geotechnical Engineering | Porous media | Gauss’ law | Earth Sciences | Hydrogeology | Nernst–Planck equations | Civil Engineering | Mixture theory | Industrial Chemistry/Chemical Engineering | Diffusion | Classical Continuum Physics | Nernst-Planck equations | Gauss'law | ENGINEERING, CHEMICAL | MULTICOMPONENT | TRANSPORT | SWELLING POROUS-MEDIA | MULTIPHASE THERMODYNAMICS | Gauss' law | FORMULATION | ELECTROQUASISTATICS | Finite element method | Surface charge | Nonlinear equations | Constitutive relationships | Deformation | Legislation | Porous materials | Velocity distribution | Matrix methods | Ion diffusion | Constituents | Mathematical analysis | Lagrange multipliers | Constitutive equations | Law | Mathematical models | Entropy | Samhällsbyggnadsteknik | Teknik och teknologier | Engineering and Technology | Construction Management | Byggproduktion

Journal Article

Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 11/2017, Volume 33, Issue 6, pp. 1924 - 1948

To improve the convergence rate in L2 norm from suboptimal to optimal for both electrostatic potential and ionic concentrations in Poisson‐Nernst‐Planck (PNP)...

Taylor‐Hood element | Poisson‐Nernst‐Planck system | semidiscretization | mixed finite element method | full discretization | the optimal error estimate | Poisson-Nernst-Planck system | Taylor-Hood element | EXISTENCE | MATHEMATICS, APPLIED | semidis-cretization | LAGRANGIAN-MULTIPLIERS | VOLUME METHOD | APPROXIMATION | SEMICONDUCTORS | PERTURBATION | BASIC EQUATIONS | STOKES EQUATIONS | CARRIER TRANSPORT | POROUS-MEDIA | Finite element method | Analysis | Methods | Norms | Error analysis | Finite element analysis | Nonlinear programming | Mathematical analysis

Taylor‐Hood element | Poisson‐Nernst‐Planck system | semidiscretization | mixed finite element method | full discretization | the optimal error estimate | Poisson-Nernst-Planck system | Taylor-Hood element | EXISTENCE | MATHEMATICS, APPLIED | semidis-cretization | LAGRANGIAN-MULTIPLIERS | VOLUME METHOD | APPROXIMATION | SEMICONDUCTORS | PERTURBATION | BASIC EQUATIONS | STOKES EQUATIONS | CARRIER TRANSPORT | POROUS-MEDIA | Finite element method | Analysis | Methods | Norms | Error analysis | Finite element analysis | Nonlinear programming | Mathematical analysis

Journal Article

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267, 07/2018, Volume 98, Issue 7, pp. 1066 - 1085

The Cauchy's problem of the generalized Poisson‐Nernst‐Planck‐Navier‐Stokes model in dimension three is considered. First, after dividing the physical domain...

35A08 | green's function | hyperbolic‐parabolic‐elliptic system | nonlinear wave propagation | huygens' principle | 35B40 | 76N10 | hyperbolic-parabolic-elliptic system | SYSTEM | MULTIDIMENSIONS | MATHEMATICS, APPLIED | HYDRODYNAMIC MODEL | DECAY | STABILITY | DIFFUSION WAVES | WELL-POSEDNESS | ASYMPTOTIC-BEHAVIOR | MECHANICS | BOLTZMANN-EQUATION | CONVERGENCE-RATES | Models | Wave propagation | Fluid dynamics | Analysis | Green's functions | Decay rate | Computational fluid dynamics | Fluid flow | Estimates | Density | Charge distribution | Navier-Stokes equations | Mach number

35A08 | green's function | hyperbolic‐parabolic‐elliptic system | nonlinear wave propagation | huygens' principle | 35B40 | 76N10 | hyperbolic-parabolic-elliptic system | SYSTEM | MULTIDIMENSIONS | MATHEMATICS, APPLIED | HYDRODYNAMIC MODEL | DECAY | STABILITY | DIFFUSION WAVES | WELL-POSEDNESS | ASYMPTOTIC-BEHAVIOR | MECHANICS | BOLTZMANN-EQUATION | CONVERGENCE-RATES | Models | Wave propagation | Fluid dynamics | Analysis | Green's functions | Decay rate | Computational fluid dynamics | Fluid flow | Estimates | Density | Charge distribution | Navier-Stokes equations | Mach number

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 06/2014, Volume 140, Issue 22, p. 224113

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of...

CHANNELS | CELL | MEMBRANE | FIELD | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | Charge density | Time dependence | Fourier-Bessel transformations | Nonlinear equations | Partial differential equations | Fourier series | CHARGE DENSITY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | PARTIAL DIFFERENTIAL EQUATIONS | ION DENSITY | DEBYE LENGTH | ANALYTICAL SOLUTION

CHANNELS | CELL | MEMBRANE | FIELD | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | Charge density | Time dependence | Fourier-Bessel transformations | Nonlinear equations | Partial differential equations | Fourier series | CHARGE DENSITY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | APPROXIMATIONS | PARTIAL DIFFERENTIAL EQUATIONS | ION DENSITY | DEBYE LENGTH | ANALYTICAL SOLUTION

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 09/2019, Volume 2153, Issue 1

The paper deals with homogenization of the generalized Poisson–Nernst–Planck problem stated in the disconnected domain composed of solid and pore phases. The...

Organic chemistry | Nonlinear equations | Computational fluid dynamics | Homogenization | Chemical reactions | Two phase | Stokes flow

Organic chemistry | Nonlinear equations | Computational fluid dynamics | Homogenization | Chemical reactions | Two phase | Stokes flow

Journal Article

Kinetic and Related Models, ISSN 1937-5093, 2018, Volume 11, Issue 1, pp. 119 - 135

In this paper a mathematical model generalizing Poisson-Nernst-Planck system is considered. The generalized model presents electrokinetics of species in a...

Mass balance | Nonlinear boundary reaction | Interface jump | Generalized Poisson-Nernst-Planck model | Energy and entropy estimates | MATHEMATICS | NONEQUILIBRIUM | MATHEMATICS, APPLIED | ION BATTERIES | mass balance | EQUATIONS | FLUX | interface jump | nonlinear boundary reaction | energy and entropy estimates

Mass balance | Nonlinear boundary reaction | Interface jump | Generalized Poisson-Nernst-Planck model | Energy and entropy estimates | MATHEMATICS | NONEQUILIBRIUM | MATHEMATICS, APPLIED | ION BATTERIES | mass balance | EQUATIONS | FLUX | interface jump | nonlinear boundary reaction | energy and entropy estimates

Journal Article

Operator Theory: Advances and Applications, ISSN 0255-0156, 2017, Volume 258, pp. 173 - 191

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 10/2016, Volume 31, pp. 210 - 226

In this paper, we investigate some sufficient conditions for the breakdown of local smooth solutions to the three dimensional nonlinear nonlocal dissipative...

Navier–Stokes equations | Electro-hydrodynamics | Nonlinear dissipative system | Blow-up criteria | Poisson–Nernst–Planck equations | Poisson-Nernst-Planck equations | Navier-Stokes equations | MATHEMATICS, APPLIED | BESOV-SPACES | WELL-POSEDNESS | ILL-POSEDNESS | SIMULATION | TRANSPORT | FLUID | REGULARITY | ACTUATORS | WEAK SOLUTIONS | Fluid dynamics | Analysis | Models | Mathematical analysis | Dissipation | Breakdown | Nonlinearity | Mathematical models | Criteria | Three dimensional

Navier–Stokes equations | Electro-hydrodynamics | Nonlinear dissipative system | Blow-up criteria | Poisson–Nernst–Planck equations | Poisson-Nernst-Planck equations | Navier-Stokes equations | MATHEMATICS, APPLIED | BESOV-SPACES | WELL-POSEDNESS | ILL-POSEDNESS | SIMULATION | TRANSPORT | FLUID | REGULARITY | ACTUATORS | WEAK SOLUTIONS | Fluid dynamics | Analysis | Models | Mathematical analysis | Dissipation | Breakdown | Nonlinearity | Mathematical models | Criteria | Three dimensional

Journal Article

Continuum Mechanics and Thermodynamics, ISSN 0935-1175, 3/2013, Volume 25, Issue 2, pp. 273 - 310

In this paper, we develop a physics-based model for the charge dynamics of ionic polymer metal composites (IPMCs) in response to mechanical deformations. The...

Matched asymptotic expansion | Poisson–Nernst–Planck | Engineering Thermodynamics, Heat and Mass Transfer | Double-layer capacitance | Ionic polymer metal composite | Finite element analysis | Theoretical and Applied Mechanics | Structural Materials | Physics | Classical Continuum Physics | Sensor | Poisson-Nernst-Planck | ARTIFICIAL MUSCLES | MECHANICS | BIOMIMETIC SENSORS | THERMODYNAMICS | TRANSDUCERS | LINEAR ELECTROMECHANICAL MODEL | ACTUATORS | Finite element method | Composite materials industry | Analysis | Polymer industry | Universities and colleges | Electric power production | Polymers | Electric properties | Aerospace engineering | Ions | Nonlinear equations | Composite materials | Metals | Electric potential | Nonlinear dynamics | Polymer matrix composites | Mathematical analysis | Exact solutions | Nonlinearity | Mathematical models | Dynamical systems

Matched asymptotic expansion | Poisson–Nernst–Planck | Engineering Thermodynamics, Heat and Mass Transfer | Double-layer capacitance | Ionic polymer metal composite | Finite element analysis | Theoretical and Applied Mechanics | Structural Materials | Physics | Classical Continuum Physics | Sensor | Poisson-Nernst-Planck | ARTIFICIAL MUSCLES | MECHANICS | BIOMIMETIC SENSORS | THERMODYNAMICS | TRANSDUCERS | LINEAR ELECTROMECHANICAL MODEL | ACTUATORS | Finite element method | Composite materials industry | Analysis | Polymer industry | Universities and colleges | Electric power production | Polymers | Electric properties | Aerospace engineering | Ions | Nonlinear equations | Composite materials | Metals | Electric potential | Nonlinear dynamics | Polymer matrix composites | Mathematical analysis | Exact solutions | Nonlinearity | Mathematical models | Dynamical systems

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2015, Volume 38, Issue 16, pp. 3575 - 3586

A steady‐state Poisson–Nernst–Planck system is investigated, which is conformed into a nonlinear Poisson equation by means of the Boltzmann statistics. It...

Boltzmann statistics | nonlinear Poisson equation | singular perturbation | super‐asymptotics | electro‐chemistry | photovoltaic | asymptotic analysis | steady‐state Poisson–Nernst–Planck system | porous media | electro-chemistry | steady-state Poisson-Nernst-Planck system | super-asymptotics | MATHEMATICS, APPLIED | Porous media | Approximation | Mathematical analysis | Nonlinearity | Constants | Boundaries | Statistics | Three dimensional

Boltzmann statistics | nonlinear Poisson equation | singular perturbation | super‐asymptotics | electro‐chemistry | photovoltaic | asymptotic analysis | steady‐state Poisson–Nernst–Planck system | porous media | electro-chemistry | steady-state Poisson-Nernst-Planck system | super-asymptotics | MATHEMATICS, APPLIED | Porous media | Approximation | Mathematical analysis | Nonlinearity | Constants | Boundaries | Statistics | Three dimensional

Journal Article

Applicable Analysis, ISSN 0003-6811, 12/2016, Volume 95, Issue 12, pp. 2661 - 2682

A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model...

Boltzmann statistics | 35B27 | 78A57 | 35J60 | 82B24 | Electro-kinetic | interfacial jump | steady-state Poisson-Nernst-Planck system | Robin condition | nonlinear Poisson equation | error corrector | oscillating coefficients | homogenisation | steady-state Poisson–Nernst–Planck system | MATHEMATICS, APPLIED | ION BATTERIES | MODEL | NERNST-PLANCK EQUATIONS | CRACKS | TRANSPORT | CONDUCTION | POROUS-MEDIA | DOMAINS | CONTACT RESISTANCE | Homogenization | Boundary conditions | Kinetics | Applied mathematics | Mathematical analysis | Discontinuity | Ion concentration | Mathematical models | Two materials | Estimates | Stems | Homogenizing

Boltzmann statistics | 35B27 | 78A57 | 35J60 | 82B24 | Electro-kinetic | interfacial jump | steady-state Poisson-Nernst-Planck system | Robin condition | nonlinear Poisson equation | error corrector | oscillating coefficients | homogenisation | steady-state Poisson–Nernst–Planck system | MATHEMATICS, APPLIED | ION BATTERIES | MODEL | NERNST-PLANCK EQUATIONS | CRACKS | TRANSPORT | CONDUCTION | POROUS-MEDIA | DOMAINS | CONTACT RESISTANCE | Homogenization | Boundary conditions | Kinetics | Applied mathematics | Mathematical analysis | Discontinuity | Ion concentration | Mathematical models | Two materials | Estimates | Stems | Homogenizing

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 12/2017, Volume 27, Issue 6, pp. 1971 - 2000

We report here new electrical laws, derived from nonlinear electrodiffusion theory, about the effect of the local geometrical structure, such as curvature, on...

35B25 | Nonelectroneutrality | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Neurobiology | 35B44 | Mathematics | Nonlinear partial differential equation | Asymptotics | 35J66 | Cusp–shaped funnel | 92C37 | Poisson–Nernst–Planck | 92C05 | Analysis | Mobius conformal map | Mathematical and Computational Engineering | Electro-diffusion | Electrolytes | Curvature | MATHEMATICS, APPLIED | MEMBRANE | Cusp-shaped funnel | CURRENTS | MODEL | PHYSICS, MATHEMATICAL | TRANSPORT | MECHANICS | Poisson-Nernst-Planck | DIFFUSION | IONIC CHANNELS | Physiological aspects | Electric fields | Differential equations | Electric properties | Neurophysiology

35B25 | Nonelectroneutrality | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Neurobiology | 35B44 | Mathematics | Nonlinear partial differential equation | Asymptotics | 35J66 | Cusp–shaped funnel | 92C37 | Poisson–Nernst–Planck | 92C05 | Analysis | Mobius conformal map | Mathematical and Computational Engineering | Electro-diffusion | Electrolytes | Curvature | MATHEMATICS, APPLIED | MEMBRANE | Cusp-shaped funnel | CURRENTS | MODEL | PHYSICS, MATHEMATICAL | TRANSPORT | MECHANICS | Poisson-Nernst-Planck | DIFFUSION | IONIC CHANNELS | Physiological aspects | Electric fields | Differential equations | Electric properties | Neurophysiology

Journal Article

Nonlinearity, ISSN 0951-7715, 06/2015, Volume 28, Issue 6, pp. 1963 - 2001

The global-in-time existence of bounded weak solutions to a large class of physically relevant, strongly coupled parabolic systems exhibiting a formal...

cross-diffusion systems | global existence analysis | nonlinear parabolic systems | entropy method | DISSIPATION | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | CONFINED GEOMETRIES | CHEMOTAXIS | EQUATIONS | PHYSICS, MATHEMATICAL | PARABOLIC-SYSTEMS | CONVERGENCE | POPULATION-MODEL | ION FLUX | POISSON-NERNST-PLANCK | Computational fluid dynamics | Fluid flow | Maximum principle | Mathematical models | Transformations | Entropy | Diffusion | Density

cross-diffusion systems | global existence analysis | nonlinear parabolic systems | entropy method | DISSIPATION | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | CONFINED GEOMETRIES | CHEMOTAXIS | EQUATIONS | PHYSICS, MATHEMATICAL | PARABOLIC-SYSTEMS | CONVERGENCE | POPULATION-MODEL | ION FLUX | POISSON-NERNST-PLANCK | Computational fluid dynamics | Fluid flow | Maximum principle | Mathematical models | Transformations | Entropy | Diffusion | Density

Journal Article