Formally gradient reaction-diffusion systems in Rn have zero spatio-temporal topological

Pages: 960 - 966, Issue Special, July 2003

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Zelik S. - Université de Poitiers, Laboratoire d’Applications des Mathématiques - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, 86962 Chasseneuil Futuroscope Cedex, France (email)

Abstract: We prove that the spatio-temporal topological entropy (= the topological entropy per unit volume) is equal to zero for formally gradient reaction-diffusion systems in $\mathbb(R)^n$. This result generalizes the well-known fact that gradient ODEs have zero topological entropy.

Keywords:  Reaction-diffusion systems, unbounded domains, formally gradient systems, topological entropy.
Mathematics Subject Classification:  35B40, 35B45.

Received: August 2002; Published: April 2003.