# Reaction-diffusion systems of Maxwell-Stefan type with reversible mass-action kinetics

@article{Herberg2013ReactiondiffusionSO, title={Reaction-diffusion systems of Maxwell-Stefan type with reversible mass-action kinetics}, author={Martin Herberg and M. Meyries and Jan Prǔss and Mathias Wilke}, journal={arXiv: Analysis of PDEs}, year={2013} }

## 43 Citations

### Exponential Time Decay of Solutions to Reaction-Cross-Diffusion Systems of Maxwell–Stefan Type

- MathematicsArchive for rational mechanics and analysis
- 2020

The key elements of the proof are the existence of a unique detailed-balance equilibrium and the derivation of an inequality relating the entropy and the entropy production.

### Analysis of Maxwell–Stefan systems for heat conducting fluid mixtures

- PhysicsNonlinear Analysis: Real World Applications
- 2021

### Analysis of an Incompressible Navier–Stokes–Maxwell–Stefan System

- Mathematics
- 2013

The Maxwell–Stefan equations for the molar fluxes, supplemented by the incompressible Navier–Stokes equations governing the fluid velocity dynamics, are analyzed in bounded domains with no-flux…

### On the Maxwell-Stefan diffusion limit for a reactive mixture of polyatomic gases in non-isothermal setting

- Mathematics, PhysicsKinetic & Related Models
- 2020

In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of the model are derived…

### Modeling and analysis of reactive multi-component two-phase flows with mass transfer and phase transition the isothermal incompressible case

- Mathematics
- 2017

Isothermal incompressible multi-component two-phase flows with mass transfer, chemical reactions, and phase transition are modeled based on first principles. It is shown that the resulting system is…

### Global–in–time existence for liquid mixtures subject to a generalised incompressibility constraint

- MathematicsJournal of Mathematical Analysis and Applications
- 2021

### Convergence of an implicit Euler Galerkin scheme for Poisson-Maxwell-Stefan systems

- Mathematics
- 2018

A fully discrete Galerkin scheme for a thermodynamically consistent transient Maxwell–Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is…

### An entropy structure preserving space-time Galerkin method for cross-diffusion systems

- Mathematics
- 2020

Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and…

### Convergence of an implicit Euler Galerkin scheme for Poisson–Maxwell–Stefan systems

- MathematicsAdv. Comput. Math.
- 2019

A fully discrete Galerkin scheme for a thermodynamically consistent transient Maxwell–Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is investigated and the existence of solutions and the convergence of a subsequence to a solution to the continuous system is proved.

## References

SHOWING 1-10 OF 31 REFERENCES

### Existence Analysis of Maxwell-Stefan Systems for Multicomponent Mixtures

- MathematicsSIAM J. Math. Anal.
- 2013

Key ideas of the proofs are the Perron-Frobenius theory for quasi-positive matrices, entropy-dissipation methods, and a new entropy variable formulation allowing for the proof of nonnegative lower and upper bounds for the concentrations.

### General mass action kinetics

- Biology
- 1972

The principal result of this work shows that there exists a simply identifiable class of kinetic expressions, including the familiar detailed balanced kinetics as a proper subclass, which ensure consistency with the extended thermodynamic conditions.

### Global existence and fast-reaction limit in reaction-diffusion systems with cross effects

- Mathematics
- 2012

This thesis is devoted to the study of parabolic systems of partial differential equations arising in mass action kinetics chemistry, population dynamics and electromigration theory. We are…

### Continuum thermodynamics of chemically reacting fluid mixtures

- Physics
- 2013

We consider viscous, heat-conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all…

### On the Maxwell-Stefan Approach to Multicomponent Diffusion

- Mathematics
- 2011

We consider the system of Maxwell-Stefan equations which describe multicomponent diffusive fluxes in non-dilute solutions or gas mixtures. We apply the Perron-Frobenius theorem to the irreducible and…

### Global Existence in Reaction-Diffusion Systems with Control of Mass: a Survey

- Mathematics
- 2010

The goal of this paper is to describe the state of the art on the question of global existence of solutions to reaction-diffusion systems for which two main properties hold: on one hand, the…

### Multicomponent flow modeling

- Mathematics
- 1999

We present multicomponent flow models derived from the kinetic theory of gases and investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial differential equations.…

### Approximate solutions to a model of two-component reactive flow

- Mathematics
- 2014

We consider a model of motion of binary mixture, based on the compressible Navier-Stokes system. The mass balances of chemically reacting species are described by the reaction-diffusion equations…

### A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations

- Mathematics, Physics
- 2012

We consider the Maxwell-Stefan model of diffusion in a multicomponent gaseous mixture. After focusing on the main differences with the Fickian diffusion model, we study the equations governing a…