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

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10.1007/s00245-022-09824-9

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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.",

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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

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Periodic Solutions of a Phase-Field Model with Hysteresis

Abstract

Keywords

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