✦ LIBER ✦

Automatic control of the temperature in thermoviscoelasticity

✍ Scribed by Maurizio Grasselli

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 178 KB
Volume: 22
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(19991110)22:16<1447::aid-mma87>3.0.co;2-6

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✦ Synopsis

A viscoelastic body which undergoes a thermomechanical process is considered. The evolution of the state variables, i.e., the displacement and temperature "elds, is described by a coupled hyperbolic}parabolic integrodi!erential system. The heat #ux through a portion of the boundary is controlled automatically by a thermostat device acting on the external temperature according to suitable measurements of the boundary strain and/or the boundary temperature. Two types of control are analysed: relay switch and Preisach hysteresis operator. In both cases, the resulting model is an initial and boundary value problem for the evolution system with non-linear and non-local boundary conditions for the temperature. Existence and uniqueness results are proved.

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