Chaos for the Hyperbolic Bioheat Equation

J. Alberto Conejero; Francisco Rodenas; Macarena Trujillo

doi:10.3934/dcds.2015.35.653

Article Contents

2015, Volume 35, Issue 2: 653-668. Doi: 10.3934/dcds.2015.35.653

This issue Previous Article Classical operators on the Hörmander algebras Next Article Bifurcation values for a family of planar vector fields of degree five

Chaos for the Hyperbolic Bioheat Equation

1.
Dept. Matemàtica Aplicada and IUMPA, Universitat Politècnica de València, València, 46022

Received: June 30, 2013

Revised: December 31, 2013

Published: January 2015

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Abstract

The Hyperbolic Heat Transfer Equation describes heat processes in which extremely short periods of time or extreme temperature gradients are involved. It is already known that there are solutions of this equation which exhibit a chaotic behaviour, in the sense of Devaney, on certain spaces of analytic functions with certain growth control. We show that this chaotic behaviour still appears when we add a source term to this equation, i.e. in the Hyperbolic Bioheat Equation. These results can also be applied for the Wave Equation and for a higher order version of the Hyperbolic Bioheat Equation.

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Mathematics Subject Classification: Primary: 47A16; Secondary: 47D06.

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