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

Michele Colturato

Applications of Mathematics (2016)

  • Volume: 61, Issue: 6, page 623-650
  • ISSN: 0862-7940

Abstract

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We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.

How to cite

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Colturato, Michele. "Solvability of a class of phase field systems related to a sliding mode control problem." Applications of Mathematics 61.6 (2016): 623-650. <http://eudml.org/doc/287546>.

@article{Colturato2016,
abstract = {We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.},
author = {Colturato, Michele},
journal = {Applications of Mathematics},
keywords = {phase transition problem; phase field system; nonlinear parabolic boundary value problem; existence; continuous dependence; phase transition problem; phase field system; nonlinear parabolic boundary value problem; existence; continuous dependence},
language = {eng},
number = {6},
pages = {623-650},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solvability of a class of phase field systems related to a sliding mode control problem},
url = {http://eudml.org/doc/287546},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Colturato, Michele
TI - Solvability of a class of phase field systems related to a sliding mode control problem
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 6
SP - 623
EP - 650
AB - We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
LA - eng
KW - phase transition problem; phase field system; nonlinear parabolic boundary value problem; existence; continuous dependence; phase transition problem; phase field system; nonlinear parabolic boundary value problem; existence; continuous dependence
UR - http://eudml.org/doc/287546
ER -

References

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