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We consider a class of cross diffusion systems with degenerate (or porous media type) diffusion which is inspired by models in mathematical biology/ecology with zero self diffusions. Known techniques for scalar equations are no longer…

Analysis of PDEs · Mathematics 2019-09-12 Dung Le

The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemical is present in a bounded vessel…

Analysis of PDEs · Mathematics 2026-04-06 The Tuan Hoang , Nhu Phong Tham , Bao Quoc Tang

The convergence to equilibrium of renormalized solutions to reaction-cross-diffusion systems in a bounded domain under no-flux boundary conditions is studied. The reactions model complex balanced chemical reaction networks coming from…

Analysis of PDEs · Mathematics 2018-08-20 Esther S. Daus , Bao Quoc Tang

We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…

Condensed Matter · Physics 2016-08-31 Horatiu Simon

A reaction-kinetic model for a two-species gas mixture undergoing pair generation and recombination reactions is considered on a flat torus. For dominant scattering with a non-moving constant-temperature background the macroscopic limit to…

Analysis of PDEs · Mathematics 2023-08-07 Gianluca Favre , Marlies Pirner , Christian Schmeiser

The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…

Analysis of PDEs · Mathematics 2020-07-03 Virginie Ehrlacher , Greta Marino , Jan-Frederik Pietschmann

We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models…

Analysis of PDEs · Mathematics 2016-04-26 E. C. M. Crooks , D. Hilhorst

In this article we study a chemical reaction-diffusion system with $m$ unknown concentration. The non-linearity in our study comes from a particular chemical reaction where one unit of a particular species generated from other $m-1$ species…

Analysis of PDEs · Mathematics 2024-07-02 Saumyajit Das

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

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…

Analysis of PDEs · Mathematics 2024-12-17 Laurent Desvillettes , Kim Dang Phung , Bao Quoc Tang

In this work, we investigate a reaction-diffusion system in which both species are influenced by self-diffusion. Due to Hopf's boundary lemma, we obtain the boundedness of the classical solution of the system. By considering a particular…

Analysis of PDEs · Mathematics 2024-04-22 Ningning Zhu , Dongpo Hu , Huili Bi

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are…

Biological Physics · Physics 2009-11-07 Sandip Kar , Suman Kumar Banik , Deb Shankar Ray

The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…

Analysis of PDEs · Mathematics 2019-09-04 Li Chen , Esther S. Daus , Ansgar Jüngel

This work introduces a new class of cross-diffusion systems for studying overcrowding dispersal of two species. The approach, based on proximal minimization energy through a minimum flow process, offers a potential generalization of…

Analysis of PDEs · Mathematics 2024-05-27 Noureddine Igbida

This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the…

Analysis of PDEs · Mathematics 2013-02-06 Laurent Desvillettes , Thomas Lepoutre , Ayman Moussa

We have previously discussed the one-dimensional multitrap system of finite range and found the somewhat unexpected result that the larger is the number of imperfect traps the higher is the transmission through them. We discuss in this work…

Classical Physics · Physics 2009-11-07 D. Bar

A reaction-diffusion equation on a family of three dimensional thin domains, collapsing onto a two dimensional subspace, is considered. In \cite{\rfa pr..} it was proved that, as the thickness of the domains tends to zero, the solutions of…

Analysis of PDEs · Mathematics 2007-05-23 T. Elsken , M. Prizzi

We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…

Analysis of PDEs · Mathematics 2015-12-29 Klemens Fellner , El-Haj Laamri

In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…

Analysis of PDEs · Mathematics 2021-09-10 William E Fitzgibbon , Jeff Morgan , Bao Quoc Tang , Hong-Ming Yin

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