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Periodic Solutions of a Phase-Field Model with Hysteresis

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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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Acknowledgements

The authors want to thank the anonymous referees for their valuable suggestions and remarks which helped to improve the manuscript.

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Authors and Affiliations

  1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Chen Bin & Sergey A. Timoshin

  2. Matrosov Institute for System Dynamics and Control Theory, Russian Academy of Sciences, Lermontov str. 134, Irkutsk, Russia, 664033

    Sergey A. Timoshin

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  1. Chen Bin
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  2. Sergey A. Timoshin
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Supported by National Natural Science Foundation of China (12071165 and 62076104), Natural Science Foundation of Fujian Province (2020J01072), Program for Innovative Research Team in Science and Technology in Fujian Province University, Quanzhou High-Level Talents Support Plan (2017ZT012), Scientific Research Fund of Huaqiao University (605-50Y19017 and 605-50Y14040). The research of the second author was also supported in part by RFBR Grant No. 18-01-00026.

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Bin, C., Timoshin, S.A. Periodic Solutions of a Phase-Field Model with Hysteresis. Appl Math Optim 85, 4 (2022). https://doi.org/10.1007/s00245-022-09824-9

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