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We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete…

Analysis of PDEs · Mathematics 2025-04-10 Georg Heinze , Alexander Mielke , Artur Stephan

The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…

Analysis of PDEs · Mathematics 2017-10-11 E. S. Daus , L. Desvillettes , A. Jüngel

We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…

Analysis of PDEs · Mathematics 2021-06-30 Thierry Gallay , Sinisa Slijepcevic

We consider a system of two reaction-diffusion equations coming out of reversible chemistry. When the reaction happens on the totality of the domain, it is known that exponential convergence to equilibrium holds. We show in this paper that…

Analysis of PDEs · Mathematics 2021-08-31 Laurent Desvillettes , Kim Dang Phung

The close-to-equilibrium regularity of solutions to a class of reaction-diffusion systems is investigated. The considered systems typically arise from chemical reaction networks and satisfy a complex balanced condition. Under some…

Analysis of PDEs · Mathematics 2017-11-29 Bao Quoc Tang

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability…

Molecular Networks · Quantitative Biology 2011-05-11 Gabor Szederkenyi , Katalin M. Hangos

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient…

Analysis of PDEs · Mathematics 2018-10-16 Jan Haskovec , Sabine Hittmeir , Peter Markowich , Alexander Mielke

In this paper, we provide a graphic formulation of non-isothermal reaction systems and show that a non-isothermal detailed balanced network system converges (locally) asymptotically to the unique equilibrium within the invariant manifold…

Dynamical Systems · Mathematics 2020-10-01 Zhou Fang , Arjan van der Schaft , Chuanhou Gao

Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects in a way that total charge and energy are conserved. The…

Analysis of PDEs · Mathematics 2026-04-09 Katharina Hopf , Michael Kniely , Alexander Mielke

We consider a thermodynamically correct framework for electro-energy-reaction-diffusion systems, which feature a monotone entropy functional while conserving the total charge and the total energy. For these systems, we construct a relative…

Analysis of PDEs · Mathematics 2025-08-08 Michael Kniely

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…

Probability · Mathematics 2025-07-15 Francesca Arceci , Francesco Carlo De Vecchi , Daniela Morale , Stefania Ugolini

We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and…

Analysis of PDEs · Mathematics 2008-08-05 R. Eymard , D. Hilhorst , M. Olech

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review…

Statistical Mechanics · Physics 2017-08-21 Marcus Kaiser , Robert L. Jack , Johannes Zimmer

This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…

Analysis of PDEs · Mathematics 2026-04-01 Hideki Murakawa , Florian Salin

We propose a kinetic relaxation-model to describe a generation-recombination reaction of two species. The decay to equilibrium is studied by two recent methods for proving hypocoercivity of the linearized equations. Exponential decay of…

Analysis of PDEs · Mathematics 2015-03-20 Lukas Neumann , Christian Schmeiser

For many real physico-chemical complex systems detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and heterogeneous catalytic oxidation. Most complex enzyme reactions…

Statistical Mechanics · Physics 2013-01-17 A. N. Gorban , E. M. Mirkes , G. S. Yablonsky

The detailed balance property is a fundamental property that must be satisfied in all the macroscopic systems with a well defined temperature at each point. On the other hand, many biochemical networks work in non-equilibrium conditions and…

Classical Analysis and ODEs · Mathematics 2025-02-10 E. Franco , J. J. L. Velázquez

Non-reciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we…

Statistical Mechanics · Physics 2022-11-28 Ziluo Zhang , Rosalba Garcia-Millan

In this article we study a reaction diffusion system with $m$ unknown concentration. The non-linearity in our study comes from an underlying reversible chemical reaction and triangular in nature. Our objective is to understand the large…

Analysis of PDEs · Mathematics 2024-11-15 Saumyajit Das , Harsha Hutridurga

We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where…

Analysis of PDEs · Mathematics 2020-12-02 Jan Maas , Alexander Mielke