Complicated dynamics of parabolic equations

with simple gradient dependence

Authors:
Martino Prizzi and Krzysztof P. Rybakowski

Journal:
Trans. Amer. Math. Soc. **350** (1998), 3119-3130

MSC (1991):
Primary 35K20; Secondary 35B40

DOI:
https://doi.org/10.1090/S0002-9947-98-02294-6

MathSciNet review:
1491875

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a smooth bounded domain. Given positive integers , and , , ..., , consider the semilinear parabolic equation

where and are smooth functions. By refining and extending previous results of Polácik we show that arbitrary -jets of vector fields in can be realized in equations of the form (E). In particular, taking we see that very complicated (chaotic) behavior is possible for reaction-diffusion-convection equations with linear dependence on .

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Additional Information

**Martino Prizzi**

Affiliation:
SISSA, via Beirut 2-4, 34013 Trieste, Italy

Email:
prizzi@sissa.it

**Krzysztof P. Rybakowski**

Affiliation:
Universität Rostock, Fachbereich Mathematik, Universitätsplatz 1, 18055 Rostock, Germany

Email:
krzysztof.rybakowski@mathematik.uni-rostock.de

DOI:
https://doi.org/10.1090/S0002-9947-98-02294-6

Keywords:
Center manifolds,
jet realization,
parabolic equations,
chaos.

Received by editor(s):
May 16, 1996

Additional Notes:
The research of the second author was supported, in part by MURST 40% and in part by the project Reaction-Diffusion Equations, Contract no. ERB CHRX CT 930 409, of the Human Capital and Mobility Programme of the European Communities

Article copyright:
© Copyright 1998
American Mathematical Society