American Institute of Mathematical Sciences

Advanced
October  1997, 3(4): 541-564. doi: 10.3934/dcds.1997.3.541

A global existence theorem for two coupled semilinear diffusion equations from climate modeling

Olaf Hansen 1,

1. 

Department of Mathematics, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany

Received  June 1996 Published  July 1997

A global existence theorem for two semilinear diffusion equations is proved. The equations are coupled and the diffusion coefficients are not uniformly elliptic. They arise in the study of a simple zonally averaged climate model (See also [8, 9, 13, 14]). The sectoriality of the diffusion operator is proved with the help of a technique of F. Ali Mehmeti and S. Nicaise [2]. Some imbedding results for weighted Sobolev spaces and sign conditions for the nonlinearities allow the application of a result due to Amann [3], which proves the global result.
Keywords: Nonlinear parabolic equations, coupled system, climate modeling., spectral theory.
Mathematics Subject Classification: 35K15, 35K55, 35P0.
Citation: Olaf Hansen. A global existence theorem for two coupled semilinear diffusion equations from climate modeling. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 541-564. doi: 10.3934/dcds.1997.3.541
[1]

Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 703-723. doi: 10.3934/dcds.2006.15.703
[2]

Bopeng Rao, Zhuangyi Liu. A spectral approach to the indirect boundary control of a system of weakly coupled wave equations. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399
[3]

Wenxiong Chen, Congming Li, Eric S. Wright. On a nonlinear parabolic system-modeling chemical reactions in rivers. Communications on Pure and Applied Analysis, 2005, 4 (4) : 889-899. doi: 10.3934/cpaa.2005.4.889
[4]

Francisco Ortegón Gallego, María Teresa González Montesinos. Existence of a capacity solution to a coupled nonlinear parabolic--elliptic system. Communications on Pure and Applied Analysis, 2007, 6 (1) : 23-42. doi: 10.3934/cpaa.2007.6.23
[5]

Chunlai Mu, Zhaoyin Xiang. Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux. Communications on Pure and Applied Analysis, 2007, 6 (2) : 487-503. doi: 10.3934/cpaa.2007.6.487
[6]

Brahim Allal, Abdelkarim Hajjaj, Jawad Salhi, Amine Sbai. Boundary controllability for a coupled system of degenerate/singular parabolic equations. Evolution Equations and Control Theory, 2022, 11 (5) : 1579-1604. doi: 10.3934/eect.2021055
[7]

Ka Kit Tung. Simple climate modeling. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 651-660. doi: 10.3934/dcdsb.2007.7.651
[8]

Inez Fung. Challenges of climate modeling. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 543-551. doi: 10.3934/dcdsb.2007.7.543
[9]

Yang Liu, Wenke Li. A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4367-4381. doi: 10.3934/dcdss.2021112
[10]

Mohamed Fadili. Controllability of a backward stochastic cascade system of coupled parabolic heat equations by one control force. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2022037
[11]

Louis Tebou. Stabilization of some coupled hyperbolic/parabolic equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1601-1620. doi: 10.3934/dcdsb.2010.14.1601
[12]

Francesca Bucci, Igor Chueshov. Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 557-586. doi: 10.3934/dcds.2008.22.557
[13]

Natalie Priebe Frank, Neil Mañibo. Spectral theory of spin substitutions. Discrete and Continuous Dynamical Systems, 2022, 42 (11) : 5399-5435. doi: 10.3934/dcds.2022105
[14]

Florian Caro, Bilal Saad, Mazen Saad. Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository. Discrete and Continuous Dynamical Systems - S, 2014, 7 (2) : 191-205. doi: 10.3934/dcdss.2014.7.191
[15]

Bopeng Rao, Xu Zhang. Frequency domain approach to decay rates for a coupled hyperbolic-parabolic system. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2789-2809. doi: 10.3934/cpaa.2021119
[16]

H. Gajewski, I. V. Skrypnik. To the uniqueness problem for nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 315-336. doi: 10.3934/dcds.2004.10.315
[17]

Jan Prüss, Gieri Simonett, Rico Zacher. On normal stability for nonlinear parabolic equations. Conference Publications, 2009, 2009 (Special) : 612-621. doi: 10.3934/proc.2009.2009.612
[18]

Wolfgang Walter. Nonlinear parabolic differential equations and inequalities. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 451-468. doi: 10.3934/dcds.2002.8.451
[19]

Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1579-1613. doi: 10.3934/dcdsb.2020174
[20]

Felipe Linares, M. Panthee. On the Cauchy problem for a coupled system of KdV equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 417-431. doi: 10.3934/cpaa.2004.3.417

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (53)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy