English
Related papers

Related papers: Fast reaction limit of reaction diffusion systems …

200 papers

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are…

Classical Analysis and ODEs · Mathematics 2009-11-11 R. K. Saxena , A. M. Mathai , H. J. Haubold

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

The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…

Analysis of PDEs · Mathematics 2025-02-25 Phuoc-Tai Nguyen , Bao Quoc Tang

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

The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…

Analysis of PDEs · Mathematics 2016-11-11 Laurent Desvillettes , Klemens Fellner , Bao Quoc Tang

We study quasilinear reaction diffusion systems relative to the Shigesada-Kawasaki-Teramoto model. Nonlinearity standing for the external force is provided with mass dissipation. Estimate in several norms of the solution is provided under…

Analysis of PDEs · Mathematics 2021-03-05 Evangelos Latos , Takashi Suzuki

We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…

Analysis of PDEs · Mathematics 2023-04-07 Alexander Mielke , Stefanie Schindler

An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…

Analysis of PDEs · Mathematics 2015-12-01 Pierluigi Colli , Takeshi Fukao

We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…

Analysis of PDEs · Mathematics 2019-11-11 Anne-Charline Chalmin , Jean-Michel Roquejoffre

We establish the existence of solutions to a class of non-linear stochastic differential equation of reaction-diffusion type in an infinite-dimensional space, with diffusion corresponding to a given transition kernel. The solution obtained…

Probability · Mathematics 2021-08-10 Conrado da Costa , Bernardo Freitas Paulo da Costa , Daniel Valesin

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 study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…

Analysis of PDEs · Mathematics 2022-04-05 Vishnu Raveendran , Emilio N. M. Cirillo , Adrian Muntean

We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry's law) posed at air-liquid interfaces. We prove the rate of convergence of the two-scale…

Numerical Analysis · Mathematics 2023-03-14 Adrian Muntean , Omar Lakkis

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 famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…

Analysis of PDEs · Mathematics 2016-07-06 Alessandro Audrito , Juan Luis Vazquez

We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the…

Analysis of PDEs · Mathematics 2020-06-24 Jeff Morgan , Bao Quoc Tang

In this paper we consider a system of three fractional differential equations describing a nonlinear reaction. Our analysis includes both analytical technique and numerical simulation. This allows us to control the efficiency of the…

Exactly Solvable and Integrable Systems · Physics 2011-11-15 Aleksander Stanislavsky

We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…

Analysis of PDEs · Mathematics 2013-10-11 Martine Marion , Roger Temam

Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in $N$-dimensions. The…

Analysis of PDEs · Mathematics 2016-08-24 P Broadbridge , BH Bradshaw-Hajek

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…

Statistical Mechanics · Physics 2009-11-11 Elisheva Cohen , David A. Kessler , Herbert Levine