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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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Additional Information

**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.