Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory |
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| Authors: | P Colli M Grasselli J Sprekels |
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| Institution: | (1) Dipartimento di Matematica, Universitàdi Pavia, Via Ferrata 1, I-27100 Pavia, Italy , IT;(2) Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi 9, I-20133 Milano, Italy , IT;(3) Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Mohrenstraß e 39, D-10117 Berlin, Germany , DE |
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| Abstract: | A hyperbolic Stefan problem based on the linearized Gurtin—Pipkin heat conduction law is considered. The temperature and
free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements
performed by real thermal sensors located within the domain containing the two-phase system and/or at its boundary. Three
different types of thermostats are analyzed: simple switch, relay switch, and a Preisach hysteresis operator. The resulting
models lead to integrodifferential hyperbolic Stefan problems with nonlinear and nonlocal boundary conditions. Existence results
are proved in all the cases. Uniqueness is also shown, except in the situation corresponding to the ideal switch.
Accepted 27 May 1997 |
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| Keywords: | , Hyperbolic Stefan problems, Heat conduction with memory, Thermostat control, Hysteresis operators of Preisach type,,,,,,AMS Classification, 35R35, 45K05, 80A22, 93B52, |
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