Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Existence, uniqueness and exponential decay: An evolution problem in heat conduction with memory

Author: Sandra Carillo
Journal: Quart. Appl. Math. 69 (2011), 635-649
MSC (2000): Primary 80A20, 74F05
DOI: https://doi.org/10.1090/S0033-569X-2011-01223-1
Published electronically: July 7, 2011
MathSciNet review: 2893993
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Abstract: A rigid linear heat conductor with memory conductor is considered. An evolution problem which arises in studying the thermodynamical state of the material with memory is considered. Specifically, the time evolution of the temperature distribution within a rigid heat conductor with memory is investigated. The constitutive equations which characterize heat conduction with memory involve an integral term since the temperature's time derivative is connected to the heat flux gradient. The integro-differential problem, when initial and boundary conditions are assigned, is studied to obtain existence and uniqueness results. Key tools turn out to be represented by suitable expressions of the minimum free energy which allow us to construct functional spaces meaningful under both the physical as well as the analytic viewpoint since therein the existence and uniqueness results can be established. Finally, conditions which guarantee exponential decay at infinity are obtained.

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Sandra Carillo
Affiliation: Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sez. Matematica S\tiny{APIENZA}, Università di Roma, I-00161 Roma, Italy
Address at time of publication: Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sez. Matematica S\tiny{APIENZA}, 16, Via A. Scarpa, 00161 Rome, Italy
Email: carillo@dmmm.uniroma1.it, sandra.carillo@uniroma1.it

DOI: https://doi.org/10.1090/S0033-569X-2011-01223-1
Received by editor(s): February 1, 2010
Published electronically: July 7, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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