English
Related papers

Related papers: Reaction-diffusion systems of Maxwell-Stefan type …

200 papers

We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions in domains with a particular geometry (annular type domains). We establish Lipschitz stability estimates in L^2…

Analysis of PDEs · Mathematics 2024-07-02 Catalin-George Lefter , Elena-Alexandra Melnig

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…

Analysis of PDEs · Mathematics 2015-12-31 Vandana Sharma , Jeff Morgan

Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…

Analysis of PDEs · Mathematics 2026-02-23 Marzia Bisi , Davide Cusseddu , Ana Jacinta Soares , Romina Travaglini

We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…

Analysis of PDEs · Mathematics 2025-06-06 Henri Berestycki , Luca Rossi , Andrea Tellini

This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…

Classical Analysis and ODEs · Mathematics 2014-09-11 R. K. Saxena , A. M. Mathai , H. J. Haubold

In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure…

Analysis of PDEs · Mathematics 2016-12-19 Klemens Fellner , Wolfgang Prager , Bao Q. Tang

We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…

Analysis of PDEs · Mathematics 2025-06-12 Yuki Tsukamoto

We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…

Analysis of PDEs · Mathematics 2022-06-14 Mohamed Majdoub , Nasser-eddine Tatar

In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a…

Statistical Mechanics · Physics 2022-07-13 Aldo Ledesma-Durán , Iván Santamaría-Holek

We investigate a kinetic model of a system in contact with several thermal reservoirs at different temperatures $T_\alpha$. Our system is a spatially uniform dilute gas whose internal dynamics is described by the nonlinear Boltzmann…

Mathematical Physics · Physics 2014-06-17 Eric A. Carlen , Joel L. Lebowitz , Clement Mouhot

We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…

Analysis of PDEs · Mathematics 2019-05-28 Brian P. Cupps , Jeff Morgan , Bao Quoc Tang

The Michaelis-Menten mechanism is probably the best known model for an enzyme-catalyzed reaction. For spatially homogeneous concentrations, QSS reductions are well known, but this is not the case when chemical species are allowed to…

Analysis of PDEs · Mathematics 2022-09-20 Martin Frank , Christian Lax , Sebastian Walcher , Olaf Wittich

The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…

Analysis of PDEs · Mathematics 2021-09-27 Klemens Fellner , Julian Fischer , Michael Kniely , Bao Quoc Tang

We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic…

Statistical Mechanics · Physics 2009-10-30 Gongwen Peng , Takao Ohta

Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…

Analysis of PDEs · Mathematics 2025-05-23 Masataka Kuwamura , Takashi Teramoto , Hideo Ikeda

This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…

Statistical Mechanics · Physics 2007-05-23 Malte Henkel

We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…

Analysis of PDEs · Mathematics 2014-10-28 A. Hoffman , H. J. Hupkes , E. Van Vleck

We consider a model describing the steady flow of compressible heat-conducting chemically-reacting multi-component mixture. We show the existence of strong solutions under the additional assumption that the mixture is sufficiently dense. We…

Analysis of PDEs · Mathematics 2020-01-01 Simon Axmann , Milan Pokorny

We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials…

Statistical Mechanics · Physics 2018-09-12 Gianmaria Falasco , Riccardo Rao , Massimiliano Esposito

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