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)

[Home Page] - [Up] - [Search] - [Help] - Created: 20010409 -