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Boundary value conditions for wave fronts in reaction-diffusion systems

Published online by Cambridge University Press:  14 November 2011

J. M. Fraile  and
J. Sabina
J. M. Fraile
Affiliation:
Departamento de Ecuaciones Funcionales, Universidad Complutense, Madrid 3, Spain
J. Sabina
Affiliation:
Departamento de Ecuaciones Funcionales, Universidad Complutense, Madrid 3, Spain
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Extract

In this paper, we introduce a new class of solutions of reaction-diffusion systems, termed directional wave front solutions. They have a propagating character and the propagation direction selects some distinguished boundary points on which we can impose boundary conditions. The Neumann and Dirichlet problems on these points are treated here in order to prove some theorems on the existence of directional wave front solutions of small amplitude, and to partially establish their asymptotic behaviour.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 127 - 136
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Chow, S. and Hale, L.. Methods of Bifurcation Theory (Berlin: Springer, 1982).CrossRefGoogle Scholar
2Fife, P.. Mathematical aspects of reacting and diffusing systems. Lecture Notes on Biomathematics 28 (Berlin: Springer, 1980).Google Scholar
3Henry, D., Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics 840 (Berlin: Springer, 1981).Google Scholar
4Kazarinoff, N., Hassard, B. and Wan, Y.. Theory and Applications of Hopf Bifurcation (London Math. Soc. Lecture Note Series 41) (Edinburgh: Cambridge University Press, 1981).Google Scholar
5Kirchgassner, K.. Homoclinic bifurcation of perturbed reversible systems. Lecture Notes in Mathematics 1017 (Berlin: Springer, 1983).Google Scholar
6Kopell, N. and Howard, L. N.. Plane wave solutions to reaction-diffusion equations. Stud. Appl. Math. 52 (1973), 291–328.CrossRefGoogle Scholar
7Murray, J. D., lectures on Nonlinear Differential Models in Biology (Oxford: Clarendon, 1977).Google Scholar
8Renardy, M.. Bifurcation of singular and transient solutions. In Recent Contributions to Non-linear Partial Differential Equations (Ed. Berestycky, L. and Brezys, H.) (London: Pitman, 1981).Google Scholar