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The stability of solutions in an initial-boundary reaction-diffusion system

Published online by Cambridge University Press:  17 April 2009

E. Tuma
Affiliation:
Department of Mathematics, Santa Maria University, PO Box 110-V Valparaiso, Chile
C.M. Blázquez
Affiliation:
Department of Mathematics, Santa Maria University, PO Box 110-V Valparaiso, Chile
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Abstract

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We study the asymptotic behaviour as t → ∞ of solutions of the initial-boundary value problem vt = G(u, v), ut = uxx + F(u, v), and t > 0, x ∈ ℝ or x ∈ ℝ+ for a wide class of initial and boundary values, where F and G are smooth functions so that the system has three rest points.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Aronson, D.G. and Weinberger, H.F., Nonlinear diffusion in population genetics, combustion and nerve conduction, Lecture Notes in Mathematics 446 (Springer-Verlag, New York, 1975).Google Scholar
[2]Klaasen, G.A. and Troy, W., ‘The stability of travelling wave front solutions of reaction diffusion system’, SIAM J. Appl. Math. 41 (1981), 145167.CrossRefGoogle Scholar
[3]Murray, J.D., Mathematical biology, Biomathematics 19 (Springer-Verlag, Berlin, Heidelberg, New York, 1989).CrossRefGoogle Scholar
[4]Rauch, J. and Smoller, J., ‘Qualitative theory of the FitzHugh-Nagumo equations’, Adv. in Math. 27 (1978), 1244.CrossRefGoogle Scholar
[5]Tuma, E., ‘Comparison principles for strongly coupled reaction diffusion equations in unbounded domains’, Proc. Roy. Soc. Edinburgh 110 (1988), 311319.CrossRefGoogle Scholar
[6]Tuma, E. and Blazquez, C.M., ‘The stability of travelling wave front solutions in an initial-boundary reaction-diffusion system’, J. Mech. App. Math, (to appear).Google Scholar