Chaos for the Hyperbolic Bioheat Equation

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2015Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete and Continuous Dynamical Systems, volume 35, pages 653-668 (issn: 1078-0947, eissn: 1553-5231,

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Authors: Conejero, J. Alberto; Rodenas, Francisco; Trujillo, Macarena;

doi: 10.3934/dcds.2015.35.653

Chaos for the Hyperbolic Bioheat Equation

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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.

The authors are supported in part by MEC and FEDER, Projects MTM2010-14909 and MTM2013-47093-P.

Related Organizations

Universitat Politècnica de València
Spain

Keywords

Chaotic C0-semigroups, One-parameter semigroups and linear evolution equations, chaotic \(C_0\)-semigroups, Hyperbolic heat equation, Applications of operator theory in the physical sciences, Cyclic vectors, hypercyclic and chaotic operators, Hypercyclic C0-semigroups, hypercyclic \(C_0\)-semigroups, Dynamics of C0- semigroups, hyperbolic heat equation, Heat and mass transfer, heat flow, dynamics of \(C_0\)-semigroups, MATEMATICA APLICADA

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