Periodic Solutions of a Phase-Field Model with Hysteresis

Chen Bin; Sergey A. Timoshin

doi:10.1007/s00245-022-09824-9

Periodic Solutions of a Phase-Field Model with Hysteresis

Chen Bin
, Sergey A. Timoshin^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

In the present paper we consider a partial differential system describing a phase-field model with temperature dependent constraint for the order parameter. The system consists of an energy balance equation with a fairly general nonlinear heat source term and a phase dynamics equation which takes into account the hysteretic character of the process. The existence of a periodic solution for this system is proved under a minimal set of assumptions on the curves defining the corresponding hysteresis region.

Original language	English
Journal	Applied Mathematics and Optimization
Volume	85
Issue number	1
DOIs	https://doi.org/10.1007/s00245-022-09824-9
Publication status	Published - Feb 2022
Externally published	Yes

Keywords

Evolution system
Hysteresis
Periodic solutions
Phase transitions

Access to Document

10.1007/s00245-022-09824-9

Cite this

@article{036d1f0068e042a7a86230e11668d444,

title = "Periodic Solutions of a Phase-Field Model with Hysteresis",

abstract = "In the present paper we consider a partial differential system describing a phase-field model with temperature dependent constraint for the order parameter. The system consists of an energy balance equation with a fairly general nonlinear heat source term and a phase dynamics equation which takes into account the hysteretic character of the process. The existence of a periodic solution for this system is proved under a minimal set of assumptions on the curves defining the corresponding hysteresis region.",

keywords = "Evolution system, Hysteresis, Periodic solutions, Phase transitions",

author = "Chen Bin and Timoshin, \{Sergey A.\}",

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/s00245-022-09824-9",

language = "English",

volume = "85",

journal = "Applied Mathematics and Optimization",

issn = "0095-4616",

number = "1",

}

TY - JOUR

T1 - Periodic Solutions of a Phase-Field Model with Hysteresis

AU - Bin, Chen

AU - Timoshin, Sergey A.

PY - 2022/2

Y1 - 2022/2

N2 - In the present paper we consider a partial differential system describing a phase-field model with temperature dependent constraint for the order parameter. The system consists of an energy balance equation with a fairly general nonlinear heat source term and a phase dynamics equation which takes into account the hysteretic character of the process. The existence of a periodic solution for this system is proved under a minimal set of assumptions on the curves defining the corresponding hysteresis region.

AB - In the present paper we consider a partial differential system describing a phase-field model with temperature dependent constraint for the order parameter. The system consists of an energy balance equation with a fairly general nonlinear heat source term and a phase dynamics equation which takes into account the hysteretic character of the process. The existence of a periodic solution for this system is proved under a minimal set of assumptions on the curves defining the corresponding hysteresis region.

KW - Evolution system

KW - Hysteresis

KW - Periodic solutions

KW - Phase transitions

UR - https://www.scopus.com/pages/publications/85124229663

U2 - 10.1007/s00245-022-09824-9

DO - 10.1007/s00245-022-09824-9

M3 - Article

AN - SCOPUS:85124229663

SN - 0095-4616

VL - 85

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

IS - 1

ER -

Periodic Solutions of a Phase-Field Model with Hysteresis

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this