Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T01:53:56.550Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison principles for strongly coupled reaction diffusion equations in unbounded domains

Published online by Cambridge University Press:  14 November 2011

E. Tuma
E. Tuma
Affiliation:
Department of Mathematical Sciences, Santa María University, P.O. Box 110-V, Valparaíso, Chile
Get access Rights & Permissions [Opens in a new window]

Synopsis

Comparison principles for systems of reaction–diffusion equations in unbounded domains and coupledvia both reaction and diffusion terms are considered. Applications are made to the FitzHugh–Nagumo equations and models of coupled nerve fibres.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 311 - 319
Copyright
Copyright © Royal Society of Edinburgh 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bell, J. and Cosner, C.. Stability Properties of a Model of Parallel Nerve Fibres. J. Differential Equations 40 (1981), 303–315.CrossRefGoogle Scholar
2Chuen, K., Conley, C. and Smoller, J.. Positively Invariant Regions for Systems of Nonlinear Diffusion Equations. Indiana Univ. Math. J. 26 (1977), 373–392.Google Scholar
3Fife, P. C. and Tang, M. M.. Comparison Principles for Reaction-Diffusion System: Irregular comparison functions and applications to questions of stability and speed of propagation of disturbances. J. Differential Equations 40 (1981), 168–185.CrossRefGoogle Scholar
4Friedman, A.. Partial Differential Equations of Parabolic Type(New Jersey: Prentice Hall, 1964).Google Scholar
5Grindrod, P. and Sleeman, B. D.. Qualitative analysis of reaction diffusion systems modelling unmyelinated nerve axons. IMA J. Math. Appl. Med. Biol. 1 (1984), 289–307.CrossRefGoogle ScholarPubMed
6Rauch, J. and Smoller, J.. Qualitative theory of the FitzHugh–Nagumo equations. Adv. in Math. 27 (1978), 12–44.CrossRefGoogle Scholar
7Rinzel, J. and Terman, D.. Propagation Phenomena in a Bistable Reaction Diffusion System. SIAM J. Appl. Math. 42 (1982), 1111–1137.CrossRefGoogle Scholar
8Sleeman, B. D. and Tuma, E.. Comparison principles for strongly coupled reaction-diffusion equations. Proc. Roy. Soc. Edinburgh Sect. A 106 (1987), 209–219.CrossRefGoogle Scholar
9Terman, D.. Comparison theorems for reaction-diffusion systems defined in an unbounded domain(Madison: University of Wisconsin, Madison Mathematics Research Center, Technical Summary Report 2374, 1982).Google Scholar