In the present contribution the sliding mode control (SMC) problem for a
phase-field model of Caginalp type is considered. First we prove the
well-posedness and some regularity results for the phase-field type state
systems modified by the state-feedback control laws. Then, we show that the
chosen SMC laws force the system to reach within finite time the sliding
manifold (that we chose in order that one of the physical variables or a
combination of them remains constant in time). We study three different types
of feedback control laws: the first one appears in the internal energy balance
and forces a linear combination of the temperature and the phase to reach a
given (space dependent) value, while the second and third ones are added in the
phase relation and lead the phase onto a prescribed target. While the control
law is non-local in space for the first two problems, it is local in the third
one, i.e., its value at any point and any time just depends on the value of the
state.Comment: Key words: phase field system, nonlinear boundary value problems,
phase transition, sliding mode control, state-feedback control la
