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

Czech Academy of Sciences
RAS - Matrosov Institute for System Dynamics and Control Theory, Siberian Branch

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",

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AU - Tolstonogov, Alexander A.

AU - Timoshin, Sergey A.

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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

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DO - 10.1007/s00030-014-0294-x

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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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