Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory

Journal Article · Sun Mar 14 23:00:00 EST 1999 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459900105· OSTI ID:21067553

Colli, P ^[1]; Grasselli, M ^[2]; Sprekels, J ^[3]

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1. Dipartimento di Matematica, Universitadi Pavia, Via Ferrata 1, I-27100 Pavia (Italy)
2. Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi 9, I-20133 Milano (Italy)
3. Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS), Mohrenstrass e 39, D-10117 Berlin (Germany)

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.

• OSTI ID: 21067553
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 39; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CONTROL THEORY
FEEDBACK
HYSTERESIS
NONLINEAR PROBLEMS
SENSORS
SWITCHES
TEMPERATURE MEASUREMENT
THERMAL CONDUCTION
THERMOSTATS