American Institute of Mathematical Sciences

Advanced
September  2010, 3(3): 427-444. doi: 10.3934/krm.2010.3.427

Asymptotic behaviour of reversible chemical reaction-diffusion equations

Ivan Gentil 1, and  Bogusław Zegarlinski 2,

1. 

Ceremade, UMR CNRS 7534, Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75775 PARIS Cedex 16
2. 

Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

Received  June 2009 Revised  April 2010 Published  July 2010

We investigate the asymptotic behavior of a large class of reversible chemical reaction-diffusion equations with the same diffusion. In particular we prove the optimal rate in two cases : when there is no diffusion and in the classical "two-by-two" case.
Keywords: Asymptotic behaviour., Reaction-diffusion equations, Poincaré inequality.
Mathematics Subject Classification: Primary: 35B40; Secondary: 28B1.
Citation: Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reaction-diffusion equations. Kinetic & Related Models, 2010, 3 (3) : 427-444. doi: 10.3934/krm.2010.3.427
[1]

Sven Jarohs, Tobias Weth. Asymptotic symmetry for a class of nonlinear fractional reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (6) : 2581-2615. doi: 10.3934/dcds.2014.34.2581
[2]

María Anguiano, P.E. Kloeden. Asymptotic behaviour of the nonautonomous SIR equations with diffusion. Communications on Pure & Applied Analysis, 2014, 13 (1) : 157-173. doi: 10.3934/cpaa.2014.13.157
[3]

Shi-Liang Wu, Tong-Chang Niu, Cheng-Hsiung Hsu. Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3467-3486. doi: 10.3934/dcds.2017147
[4]

Piermarco Cannarsa, Giuseppe Da Prato. Invariance for stochastic reaction-diffusion equations. Evolution Equations & Control Theory, 2012, 1 (1) : 43-56. doi: 10.3934/eect.2012.1.43
[5]

Martino Prizzi. A remark on reaction-diffusion equations in unbounded domains. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 281-286. doi: 10.3934/dcds.2003.9.281
[6]

Angelo Favini, Atsushi Yagi. Global existence for Laplace reaction-diffusion equations. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1-21. doi: 10.3934/dcdss.2020083
[7]

Linda J. S. Allen, B. M. Bolker, Yuan Lou, A. L. Nevai. Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 1-20. doi: 10.3934/dcds.2008.21.1
[8]

Keng Deng, Yixiang Wu. Asymptotic behavior for a reaction-diffusion population model with delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 385-395. doi: 10.3934/dcdsb.2015.20.385
[9]

Yuncheng You. Asymptotic dynamics of reversible cubic autocatalytic reaction-diffusion systems. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1415-1445. doi: 10.3934/cpaa.2011.10.1415
[10]

Keng Deng. Asymptotic behavior of an SIR reaction-diffusion model with a linear source. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 5945-5957. doi: 10.3934/dcdsb.2019114
[11]

Peter E. Kloeden, Thomas Lorenz, Meihua Yang. Reaction-diffusion equations with a switched--off reaction zone. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1907-1933. doi: 10.3934/cpaa.2014.13.1907
[12]

Jacson Simsen, Mariza Stefanello Simsen, Marcos Roberto Teixeira Primo. Reaction-Diffusion equations with spatially variable exponents and large diffusion. Communications on Pure & Applied Analysis, 2016, 15 (2) : 495-506. doi: 10.3934/cpaa.2016.15.495
[13]

Svetlana Matculevich, Pekka Neittaanmäki, Sergey Repin. A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne--Weinberger inequality. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2659-2677. doi: 10.3934/dcds.2015.35.2659
[14]

Jong-Shenq Guo, Yoshihisa Morita. Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 193-212. doi: 10.3934/dcds.2005.12.193
[15]

Ming Mei. Stability of traveling wavefronts for time-delayed reaction-diffusion equations. Conference Publications, 2009, 2009 (Special) : 526-535. doi: 10.3934/proc.2009.2009.526
[16]

Antoine Mellet, Jean-Michel Roquejoffre, Yannick Sire. Generalized fronts for one-dimensional reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 303-312. doi: 10.3934/dcds.2010.26.303
[17]

Matthieu Alfaro, Thomas Giletti. Varying the direction of propagation in reaction-diffusion equations in periodic media. Networks & Heterogeneous Media, 2016, 11 (3) : 369-393. doi: 10.3934/nhm.2016001
[18]

Wei Wang, Anthony Roberts. Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 253-273. doi: 10.3934/dcds.2011.31.253
[19]

Masaharu Taniguchi. Multi-dimensional traveling fronts in bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 1011-1046. doi: 10.3934/dcds.2012.32.1011
[20]

Filipa Caetano, Martin J. Gander, Laurence Halpern, Jérémie Szeftel. Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations. Networks & Heterogeneous Media, 2010, 5 (3) : 487-505. doi: 10.3934/nhm.2010.5.487

2018 Impact Factor: 1.38

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences