Control of a Multi-Component Phase Transition Model with Hysteresis

Chen Bin; Emil Minchev; Sergey A. Timoshin; Jin Xiaohan

doi:10.1007/s00245-022-09823-w

Control of a Multi-Component Phase Transition Model with Hysteresis

Chen Bin, Emil Minchev, Sergey A. Timoshin^*, Jin Xiaohan

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

The present paper addresses a phase-field system modelling the dynamics of solid-liquid phase transitions of several substances coexisting in the same container. We allow for a hysteretic effect in the vector order parameter—absolute temperature relationship. Our system is subjected to an external control action constrained to a nonconvex-valued mapping. The existence of solutions for this control problem is established and some of their relaxation type properties are explored under a minimal set of requirements on the curves describing the hysteresis region of the problem.

Original language	English
Journal	Applied Mathematics and Optimization
Volume	85
Issue number	1
DOIs	https://doi.org/10.1007/s00245-022-09823-w
Publication status	Published - Feb 2022
Externally published	Yes

Keywords

Control problems
Evolution systems
Hysteresis
Phase transitions
Relaxation
Well-posedness

Access to Document

10.1007/s00245-022-09823-w

Cite this

@article{d1dc223f85b5453d98f4e33370f2df3a,

title = "Control of a Multi-Component Phase Transition Model with Hysteresis",

abstract = "The present paper addresses a phase-field system modelling the dynamics of solid-liquid phase transitions of several substances coexisting in the same container. We allow for a hysteretic effect in the vector order parameter—absolute temperature relationship. Our system is subjected to an external control action constrained to a nonconvex-valued mapping. The existence of solutions for this control problem is established and some of their relaxation type properties are explored under a minimal set of requirements on the curves describing the hysteresis region of the problem.",

keywords = "Control problems, Evolution systems, Hysteresis, Phase transitions, Relaxation, Well-posedness",

author = "Chen Bin and Emil Minchev and Timoshin, {Sergey A.} and Jin Xiaohan",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = feb,

doi = "10.1007/s00245-022-09823-w",

language = "English",

volume = "85",

journal = "Applied Mathematics and Optimization",

issn = "0095-4616",

number = "1",

}

TY - JOUR

T1 - Control of a Multi-Component Phase Transition Model with Hysteresis

AU - Bin, Chen

AU - Minchev, Emil

AU - Timoshin, Sergey A.

AU - Xiaohan, Jin

PY - 2022/2

Y1 - 2022/2

N2 - The present paper addresses a phase-field system modelling the dynamics of solid-liquid phase transitions of several substances coexisting in the same container. We allow for a hysteretic effect in the vector order parameter—absolute temperature relationship. Our system is subjected to an external control action constrained to a nonconvex-valued mapping. The existence of solutions for this control problem is established and some of their relaxation type properties are explored under a minimal set of requirements on the curves describing the hysteresis region of the problem.

AB - The present paper addresses a phase-field system modelling the dynamics of solid-liquid phase transitions of several substances coexisting in the same container. We allow for a hysteretic effect in the vector order parameter—absolute temperature relationship. Our system is subjected to an external control action constrained to a nonconvex-valued mapping. The existence of solutions for this control problem is established and some of their relaxation type properties are explored under a minimal set of requirements on the curves describing the hysteresis region of the problem.

KW - Control problems

KW - Evolution systems

KW - Hysteresis

KW - Phase transitions

KW - Relaxation

KW - Well-posedness

UR - http://www.scopus.com/inward/record.url?scp=85124002137&partnerID=8YFLogxK

U2 - 10.1007/s00245-022-09823-w

DO - 10.1007/s00245-022-09823-w

M3 - Article

AN - SCOPUS:85124002137

SN - 0095-4616

VL - 85

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

IS - 1

ER -

Control of a Multi-Component Phase Transition Model with Hysteresis

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this