Preprint No.
A-01-03
Bernold Fiedler, Carlos Rocha, Domingo Salazar, Joan Sola-Morales
A Note on the Dynamics of Piecewise-Autonomous Bistable Parabolic
Equations
Abstract:
For a family of piecewise-autonomous one-dimensional bistable
parabolic equations, with vanishing diffusion and Neumann boundary
conditions, we determine the number and Morse indices of their equilibria
as a function of the number of subintervals where the equations are
autonomous. We conjecture how to build their attractors in a recursive way
as the number of subintervals increases.
Keywords: reaction-diffusion equations, Morse
index, global attractor, meander permutation
Mathematics Subject Classification (MSC2000): Primary 35K20, Secondary 37C70
Language: ENG
Available: Pr-A-01-03.ps
Pr-A-01-03.ps.gz
Contact: Bernold Fiedler, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (fiedler@math.fu-berlin.de)
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