A control problem in phase transition modeling

Pavel Krejčí; Alexander A. Tolstonogov; Sergey A. Timoshin

doi:10.1007/s00030-014-0294-x

A control problem in phase transition modeling

Pavel Krejčí, Alexander A. Tolstonogov^*, Sergey A. Timoshin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We consider a nonlinear partial differential control system describing phase transitions taking account of hysteresis effects. The control constraint is given by a multivalued mapping with nonconvex closed bounded values in a finite dimensional space depending on the phase variables. Existence of solutions and topological properties of the set of admissible “trajectory-control” pairs are discussed in detail.

Original language	English
Pages (from-to)	513-542
Number of pages	30
Journal	Nonlinear Differential Equations and Applications
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s00030-014-0294-x
Publication status	Published - 21 Aug 2015
Externally published	Yes

Keywords

Extreme points
Hysteresis
Nonconvex constraints
Nonlinear evolution control systems
Subdifferential

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10.1007/s00030-014-0294-x

Cite this

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title = "A control problem in phase transition modeling",

abstract = "We consider a nonlinear partial differential control system describing phase transitions taking account of hysteresis effects. The control constraint is given by a multivalued mapping with nonconvex closed bounded values in a finite dimensional space depending on the phase variables. Existence of solutions and topological properties of the set of admissible “trajectory-control” pairs are discussed in detail.",

keywords = "Extreme points, Hysteresis, Nonconvex constraints, Nonlinear evolution control systems, Subdifferential",

author = "Pavel Krej{\v c}{\'i} and Tolstonogov, \{Alexander A.\} and Timoshin, \{Sergey A.\}",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Basel.",

year = "2015",

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doi = "10.1007/s00030-014-0294-x",

language = "English",

volume = "22",

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AU - Krejčí, Pavel

AU - Tolstonogov, Alexander A.

AU - Timoshin, Sergey A.

PY - 2015/8/21

Y1 - 2015/8/21

N2 - We consider a nonlinear partial differential control system describing phase transitions taking account of hysteresis effects. The control constraint is given by a multivalued mapping with nonconvex closed bounded values in a finite dimensional space depending on the phase variables. Existence of solutions and topological properties of the set of admissible “trajectory-control” pairs are discussed in detail.

AB - We consider a nonlinear partial differential control system describing phase transitions taking account of hysteresis effects. The control constraint is given by a multivalued mapping with nonconvex closed bounded values in a finite dimensional space depending on the phase variables. Existence of solutions and topological properties of the set of admissible “trajectory-control” pairs are discussed in detail.

KW - Extreme points

KW - Hysteresis

KW - Nonconvex constraints

KW - Nonlinear evolution control systems

KW - Subdifferential

UR - https://www.scopus.com/pages/publications/84939562552

U2 - 10.1007/s00030-014-0294-x

DO - 10.1007/s00030-014-0294-x

M3 - Article

AN - SCOPUS:84939562552

SN - 1021-9722

VL - 22

SP - 513

EP - 542

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 4

ER -

A control problem in phase transition modeling

Abstract

Keywords

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