Calculus of Variations and Geometric Measure Theory

M. Colturato

On a class of conserved phase field systems with a maximal monotone perturbation

created by michele on 22 Apr 2017
modified on 04 May 2020


Published Paper

Inserted: 22 apr 2017
Last Updated: 4 may 2020

Journal: Appl. Math. Optim.
Pages: 41
Year: 2017
Doi: 10.1007/s00245-017-9415-3


We prove existence and regularity for the solutions to a Cahn{Hilliard system describing the phenomenon of phase separation for a material contained in a bounded and regular domain. Since the first equation of the system is perturbed by the presence of an additional maximal monotone operator, we show our results using suitable regularization of the nonlinearities of the problem and performing some a priori estimates which allow us to pass to the limit thanks to compactness and monotonicity arguments. Next, under further assumptions, we deduce a continuous dependence estimate whence the uniqueness property is also achieved. Then, we consider the related sliding mode control (SMC) problem and show that the chosen SMC law forces a suitable linear combination of the temperature and the phase to reach a given (space-dependent) value within finite time.