Automatische Steuerung freier Ränder bei Stefan-Problemen durch Thermostatkontrollen am festen Rand

Abstract

The automatic control of the free boundary in one-phase Stefan problems via the input data at the fixed boundary is considered. In contrast to previous papers concerned with this subject the thermostat controlling the input data observes the temparature at the fixed boundary instead of the evolution of the free boundary. The corresponding parabolic initial-boundary value system is nonlinear and discontinuous. Unique solvability is shown and numerical results are presented.