Automatic control of the temperature in phase change problems with memory
The author deals with a parabolic two-phase system with memory occupying a bounded and smooth domain \(\Omega\subset \mathbb{R}^N\) \((N\geq 1)\), whose state is described by the pair \((\theta,\chi)\). Here \(\theta\) is the relative temperature \((\theta=0\) being the equilibrium temperature at which the two phases, for instance solid and liquid, can coexist) and \(\chi\) is the concentration of the more energetic phase (that is water in water-ice system). Assuming on the phase variable either a relaxation dynamics or a Stefan condition, the author proves existence and uniqueness results for feedback control problems corresponding to two different types of thermostat: the relay switch and the Preisach operator. Moreover, the author shows that, when the data enjoy suitable regularity properties, one can obtain a stronger regularity for the solution.
scientific article; zbMATH DE number 1747395