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Generic properties of equilibria of reaction-diffusion equations with variable diffusion

Published online by Cambridge University Press:  14 November 2011

Carlos Rocha
Carlos Rocha
Affiliation:
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, U.S.A.
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Synopsis

It is shown that, generically, scalar one-dimensional parabolic equations ut = (a2(x)ux)x + f(u), x ∈ [0, 1], with Neumann boundary conditions, have all the equilibrium solutions hyperbolic.

Moreover, the bifurcations of these equilibria are generically of the saddle-node type.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 45 - 55
Copyright
Copyright © Royal Society of Edinburgh 1985

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