Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-16T17:37:14.053Z Has data issue: false hasContentIssue false
  • English
  • Français

Generic hyperbolicity for scalar parabolic equations

Published online by Cambridge University Press:  14 November 2011

Antonio L. Pereira
Antonio L. Pereira
Affiliation:
Instituto de Matematica e Estatística da USP, Caixa Postal 20570 Ag. Iguatemi, 01452-001 – São Paulo – SP, Brasil
Get access Rights & Permissions [Opens in a new window]

Synopsis

For the reaction diffusion equation

with homogeneous Neumann boundary conditions, we give results on the generic hyperbolicity of equilibria with respect to a for fixed f and with respect to f for fixed a.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1031 - 1040
Copyright
Copyright © Royal Society of Edinburgh 1993

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

1Brunovsky, P. and Chow, S.-N.. Generic properties of stationary solutions of reaction-diffusion equations. J. Differential Equations 53 (1984), 1–23.CrossRefGoogle Scholar
2Coddington, E. A. and Levinson, N.. Theory of Ordinary Differential Equations (New York: McGraw-Hill, 1955).Google Scholar
3Fusco, G. and Hale, J. K.. Stable equilibria in a scalar parabolic equation with variable diffusion. SIAM J. Math. Anal. 16 (1985), 1152–1164.CrossRefGoogle Scholar
4Hale, J. K. and Raugel, G.. Reaction-diffusion equations in thin domains. J. Math. Pures Appl. (to appear).Google Scholar
5Rocha, C.. Generic properties and bifurcation diagrams of scalar parabolic equations. Proc. Roy. Soc. Edinburgh Sect. A 101 (1985), 45–55.CrossRefGoogle Scholar
6Smoller, J. and Wasserman, A.. Generic bifurcation of steady-state solutions. J. Differential Equations 52 (1984), 432–438.CrossRefGoogle Scholar