IJPAM: Volume 107, No. 4 (2016)

A SYMBOLIC APPROACH TO
NONLINEARLY PERTURBED HEAT EQUATION

Carlos Correia Ramos$^1$, Ana Isabel Santos$^2$, Sandra Vinagre$^3$
$^{1,2,3}$Department of Mathematics, CIMA
University of Évora
Rua Romão Ramalho 59, 7000-671, Évora, PORTUGAL


Abstract. We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.

Received: November 23, 2015

AMS Subject Classification: 37B10, 37B40, 39B12, 35K05, 37K60, 37E05, 74H65

Key Words and Phrases: heat equation, chaotic dynamics, symbolic dynamics, iteration theory, topological entropy, complex systems

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DOI: 10.12732/ijpam.v107i4.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 4
Pages: 821 - 843


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).