Evolution systems of nonlinear variational inequalities arising from phase change problems

Regularity and convergence results for a phase-field model with memory

“…In the papers [17,18], existence, uniqueness and asymptotic results (as tP#R) were proved, for parabolic phase-field models without memory. In particular, Kenmochi and Niezgo´dka [17] considered a problem with a non-linear constraint on the phase variable, while Laureniot [18] dealt with a standard model, assuming (non-linear and) with quadratic growth.…”

“…In particular, Kenmochi and Niezgo´dka [17] considered a problem with a non-linear constraint on the phase variable, while Laureniot [18] dealt with a standard model, assuming (non-linear and) with quadratic growth. As far as we know, parabolic phase-field models with memory have not been studied yet, except for the paper [5], where the existence and the uniqueness of a solution to (1.1)-(1.4) were proved in a quite general setting (in particular, allowing to have a quadratic growth).…”

On a Conserved Penrose-Fife Type System

“…This can be done using the ideas of [17]. The reader could refer to [6, p. 283] for a detailed application which holds in the present case without any change.…”

“…Regarding non conserved models (i.e., second order phase dynamics), several papers [8], [12], [13], [16], [17], [19], [20], [30] deal with the case α(ϑ) ≈ −1/ϑ. On the other hand, less papers [10], [21] consider the Fourier law α(ϑ) ≈ ϑ, which is more satisfactory for high temperatures but leads to a more difficult problem.…”

Solvability of a class of phase field systems related to a sliding mode control problem

“…We refer, without any sake of completeness, e.g., to [4,12,14,18,19] and references therein for the well-posedness and long time behavior results and to [6-8, 15, 16] for the treatment of optimal control problems.…”