American Institute of Mathematical Sciences

Advanced
April  2001, 7(2): 377-384. doi: 10.3934/dcds.2001.7.373

Modeling chemical reactions in rivers: A three component reaction

Congming Li 1, and  Eric S. Wright 2,

1. 

Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0524, United States
2. 

Department of Applied Mathematics, University of Colorado at Boulder, Campus Box 526, Boulder, CO 80309, United States

Revised  October 2000 Published  January 2001

What follows is the analysis of a model for dynamics of chemical reactions in a river. Dominant forces to be considered include diffusion, advection, and rates of creation or destruction of participating species (due to chemical reactions). In light of this, the model we will be using will be based upon a nonlinear system of reaction-advection-diffusion equations. The nonlinearity comes solely from the influences of the chemical reactions.
First, we will establish some general results for reaction diffusion systems. In particular, we will illustrate a class of reaction diffusion systems whose solutions are bounded from below by zero. We will also provide a local existence result for this class of problems. Afterwards, we will focus on the dynamics of an equidiffusive three component reaction system. Specifically, we will provide conditions under which one could be guaranteed the existence of global solutions. We will also discuss the qualities of the $\omega$-limit set for this system.
Keywords: Reaction diffusion systems, local existence..
Mathematics Subject Classification: Primary: 35B05, 35B35, 35K4.
Citation: Congming Li, Eric S. Wright. Modeling chemical reactions in rivers: A three component reaction. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 377-384. doi: 10.3934/dcds.2001.7.373
[1]

Wei Feng, Weihua Ruan, Xin Lu. On existence of wavefront solutions in mixed monotone reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 815-836. doi: 10.3934/dcdsb.2016.21.815
[2]

Jianhua Huang, Xingfu Zou. Existence of traveling wavefronts of delayed reaction diffusion systems without monotonicity. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 925-936. doi: 10.3934/dcds.2003.9.925
[3]

Zhoude Shao. Existence and continuity of strong solutions of partly dissipative reaction diffusion systems. Conference Publications, 2011, 2011 (Special) : 1319-1328. doi: 10.3934/proc.2011.2011.1319
[4]

Aníbal Rodríguez-Bernal, Silvia Sastre-Gómez. Nonlinear nonlocal reaction-diffusion problem with local reaction. Discrete and Continuous Dynamical Systems, 2022, 42 (4) : 1731-1765. doi: 10.3934/dcds.2021170
[5]

Hideki Murakawa. Fast reaction limit of reaction-diffusion systems. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1047-1062. doi: 10.3934/dcdss.2020405
[6]

Xiongxiong Bao, Wan-Tong Li. Existence and stability of generalized transition waves for time-dependent reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3621-3641. doi: 10.3934/dcdsb.2020249
[7]

Alexey Cheskidov, Songsong Lu. The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 55-66. doi: 10.3934/dcdss.2009.2.55
[8]

Vandana Sharma. Global existence and uniform estimates of solutions to reaction diffusion systems with mass transport type boundary conditions. Communications on Pure and Applied Analysis, 2021, 20 (3) : 955-974. doi: 10.3934/cpaa.2021001
[9]

Vandana Sharma, Jyotshana V. Prajapat. Global existence of solutions to reaction diffusion systems with mass transport type boundary conditions on an evolving domain. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 109-135. doi: 10.3934/dcds.2021109
[10]

S.-I. Ei, M. Mimura, M. Nagayama. Interacting spots in reaction diffusion systems. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 31-62. doi: 10.3934/dcds.2006.14.31
[11]

Angelo Favini, Atsushi Yagi. Global existence for Laplace reaction-diffusion equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1473-1493. doi: 10.3934/dcdss.2020083
[12]

Henri Berestycki, Nancy Rodríguez. A non-local bistable reaction-diffusion equation with a gap. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 685-723. doi: 10.3934/dcds.2017029
[13]

Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515
[14]

Laurent Desvillettes, Klemens Fellner. Entropy methods for reaction-diffusion systems. Conference Publications, 2007, 2007 (Special) : 304-312. doi: 10.3934/proc.2007.2007.304
[15]

A. Dall'Acqua. Positive solutions for a class of reaction-diffusion systems. Communications on Pure and Applied Analysis, 2003, 2 (1) : 65-76. doi: 10.3934/cpaa.2003.2.65
[16]

Dieter Bothe, Michel Pierre. The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 49-59. doi: 10.3934/dcdss.2012.5.49
[17]

Md. Rabiul Haque, Takayoshi Ogawa, Ryuichi Sato. Existence of weak solutions to a convection–diffusion equation in a uniformly local lebesgue space. Communications on Pure and Applied Analysis, 2020, 19 (2) : 677-697. doi: 10.3934/cpaa.2020031
[18]

Giovany M. Figueiredo, Tarcyana S. Figueiredo-Sousa, Cristian Morales-Rodrigo, Antonio Suárez. Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3689-3711. doi: 10.3934/dcdsb.2018311
[19]

Michaël Bages, Patrick Martinez. Existence of pulsating waves in a monostable reaction-diffusion system in solid combustion. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 817-869. doi: 10.3934/dcdsb.2010.14.817
[20]

Georg Hetzer. Global existence for a functional reaction-diffusion problem from climate modeling. Conference Publications, 2011, 2011 (Special) : 660-671. doi: 10.3934/proc.2011.2011.660

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (59)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy