American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems
  • CPAA Home
  • This Issue
  • Next Article
    Boundary layers in weak solutions of hyperbolic conservation laws II. self-similar vanishing diffusion limits
March  2002, 1(1): 77-84. doi: 10.3934/cpaa.2002.1.77

Global existence of solutions to a reaction diffusion system based upon carbonate reaction kinetics

Congming Li 1, and  Eric S. Wright 2,

1. 

Department of Applied Mathematics, University of Colorado at Boulder, United States
2. 

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

Received  July 2001 Published  December 2001

The carbonate system is an important reaction system in natural waters because it plays the role of a buffer, regulating the pH of the water. We present a global existence result for a system of partial differential equations that can be used to model the combined dynamics of diffusion, advection, and the reaction kinetics of the carbonate system.
Keywords: partial differential equations, Carbonate system.
Mathematics Subject Classification: Primary: 35B35, 35B45, 35B50, 35B60, 35K45,35K57, Secondary: 80A30, 80A32, 80A50, 92E2.
Citation: Congming Li, Eric S. Wright. Global existence of solutions to a reaction diffusion system based upon carbonate reaction kinetics. Communications on Pure & Applied Analysis, 2002, 1 (1) : 77-84. doi: 10.3934/cpaa.2002.1.77
[1]

Michela Eleuteri, Pavel Krejčí. An asymptotic convergence result for a system of partial differential equations with hysteresis. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1131-1143. doi: 10.3934/cpaa.2007.6.1131
[2]

Yves Achdou, Mathieu Laurière. On the system of partial differential equations arising in mean field type control. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 3879-3900. doi: 10.3934/dcds.2015.35.3879
[3]

B. S. Goh, W. J. Leong, Z. Siri. Partial Newton methods for a system of equations. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 463-469. doi: 10.3934/naco.2013.3.463
[4]

Herbert Koch. Partial differential equations with non-Euclidean geometries. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 481-504. doi: 10.3934/dcdss.2008.1.481
[5]

Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 703-723. doi: 10.3934/dcds.2006.15.703
[6]

Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 1053-1065. doi: 10.3934/cpaa.2009.8.1053
[7]

Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 515-557. doi: 10.3934/dcdsb.2010.14.515
[8]

Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167
[9]

Barbara Abraham-Shrauner. Exact solutions of nonlinear partial differential equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 577-582. doi: 10.3934/dcdss.2018032
[10]

Paul Bracken. Exterior differential systems and prolongations for three important nonlinear partial differential equations. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1345-1360. doi: 10.3934/cpaa.2011.10.1345
[11]

Frédéric Mazenc, Christophe Prieur. Strict Lyapunov functions for semilinear parabolic partial differential equations. Mathematical Control & Related Fields, 2011, 1 (2) : 231-250. doi: 10.3934/mcrf.2011.1.231
[12]

Enrique Zuazua. Controllability of partial differential equations and its semi-discrete approximations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (2) : 469-513. doi: 10.3934/dcds.2002.8.469
[13]

Paul Bracken. Connections of zero curvature and applications to nonlinear partial differential equations. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1165-1179. doi: 10.3934/dcdss.2014.7.1165
[14]

Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295
[15]

Yuhki Hosoya. First-order partial differential equations and consumer theory. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1143-1167. doi: 10.3934/dcdss.2018065
[16]

Hernán R. Henríquez, Claudio Cuevas, Alejandro Caicedo. Asymptotically periodic solutions of neutral partial differential equations with infinite delay. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2031-2068. doi: 10.3934/cpaa.2013.12.2031
[17]

Frédéric Gibou, Doron Levy, Carlos Cárdenas, Pingyu Liu, Arthur Boyer. Partial Differential Equations-Based Segmentation for Radiotherapy Treatment Planning. Mathematical Biosciences & Engineering, 2005, 2 (2) : 209-226. doi: 10.3934/mbe.2005.2.209
[18]

Rongmei Cao, Jiangong You. The existence of integrable invariant manifolds of Hamiltonian partial differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 227-234. doi: 10.3934/dcds.2006.16.227
[19]

Seyedeh Marzieh Ghavidel, Wolfgang M. Ruess. Flow invariance for nonautonomous nonlinear partial differential delay equations. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2351-2369. doi: 10.3934/cpaa.2012.11.2351
[20]

Antonio Cañada, Salvador Villegas. Lyapunov inequalities for partial differential equations at radial higher eigenvalues. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 111-122. doi: 10.3934/dcds.2013.33.111

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (15)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences