GLOBAL SMOOTH SOLUTION FOR PHASE TRANSITION EQUATIONS IN FERROMAGNETISM

Fangfang Li; Boling Guo

doi:10.11948/20240008

2024 Volume 14 Issue 6

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(6): 3332-3348

Next Article Previous Article

Fangfang Li, Boling Guo. GLOBAL SMOOTH SOLUTION FOR PHASE TRANSITION EQUATIONS IN FERROMAGNETISM[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3332-3348. doi: 10.11948/20240008

Citation:

Fangfang Li, Boling Guo. GLOBAL SMOOTH SOLUTION FOR PHASE TRANSITION EQUATIONS IN FERROMAGNETISM[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3332-3348. doi: 10.11948/20240008

GLOBAL SMOOTH SOLUTION FOR PHASE TRANSITION EQUATIONS IN FERROMAGNETISM

Fangfang Li^1, ,,
Boling Guo^2,

1.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Author Bio: Email: gbl@iapcm.ac.cn(B. Guo)
Corresponding author: Email: liff672@nenu.edu.cn(F. Li)
Fund Project: This work is supported by National Natural Science Foundation of China (12101115, 12371216) and the Fundamental Research Funds for the Central Universities (2412021QD002)

Abstract

Abstract

This paper presents a phase transition model that characterizes the thermodynamic and electromagnetic properties of ferromagnetic materials. We establish the existence of both a global weak solution and a global smooth solution for the phase transition equations in two and three dimensions. Moreover, we obtain the uniqueness of the global smooth solution.
- Phase transition equations /
- Galerkin method /
- global smooth solution
MSC: 35Q60, 35D30, 78A25

FullText(HTML)

References

[1]	C. Ayouch, E. H. Essoufi, M. Ouhadan, et al., On a fractional phase transition model in ferromagnetism, Electron. J. Differential Equations, 2018, 175, 175–188. Google Scholar
[2]	V. Berti, M. Fabrizio and C. Giorgi, Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity, Phys. D, 2007, 236, 13–21. doi: 10.1016/j.physd.2007.07.009 CrossRef Google Scholar
[3]	V. Berti, M. Fabrizio and C. Giorgi, A three-dimensional phase transition model in ferromagnetism: Existence and uniqueness, J. Math. Anal. Appl., 2009, 355, 661–674. doi: 10.1016/j.jmaa.2009.01.065 CrossRef Google Scholar
[4]	V. Berti and D. Grandi, A non-isothermal phase-field model for the ferromagnetic transition, Math. Methods. Appl. Sci., 2013, 36(11), 1342–1349. doi: 10.1002/mma.2686 CrossRef Google Scholar
[5]	K. Buschow and F. Boer, Physics of Magnetism and Magnetic Materials, Springer, New York, 2003. Google Scholar
[6]	H. Byung-Hoon, On the derivation of the Landau-Lifshitz frame in relativistic kinetic theory, Fluid Dyn. Res., 2023, 54(1), 015501. Google Scholar
[7]	S. Chikazumi, Physics of Ferromagnetism, Oxford University Press, Oxford, 2009. Google Scholar
[8]	M. Fabrizio, Ginzburg-Landau equations and first and second order phase transitions, Internat. J. Engrg. Sci., 2006, 44, 529–539. doi: 10.1016/j.ijengsci.2006.02.006 CrossRef Google Scholar
[9]	M. Fabrizio, C. Giorgi and A. Morro, A continuum theory for first-order phase transitions based on the balance of the structure order, Math. Methods. Appl. Sci., 2008, 31, 627–653. doi: 10.1002/mma.930 CrossRef Google Scholar
[10]	U. Gianazza and N. Liao, Continuity of the temperature in a multi-phase transition problem, J. Anal. Math., 2023, 150(2), 583–607. doi: 10.1007/s11854-023-0283-2 CrossRef Google Scholar
[11]	B. L. Guo and S. J. Ding, Landau-Lifshitz Equations, World Scientific, Hackensack, New Jersey, 2008. Google Scholar
[12]	N. A. Kudryashov, Conservation laws of the complex Ginzburg-Landau equation, Phys. Lett. A, 2023, 481, 128994. doi: 10.1016/j.physleta.2023.128994 CrossRef Google Scholar
[13]	Q. X. Li, B. L. Guo, F. X. Liu and W. M. Liu, Weak and strong solutions to Landau-Lifshitz-Bloch-Maxwell equations with polarization, J. Diff. Eqs., 2021, 286, 47–83. doi: 10.1016/j.jde.2021.02.042 CrossRef Google Scholar
[14]	I. Shimizu, Local well-posedness of the Landau-Lifshitz equation with helicity term, J. Math. Phys., 2022, 63(9), 091505. doi: 10.1063/5.0087308 CrossRef Google Scholar
[15]	A. L. Soenjaya and T. Tran, Global solutions of the Landau-Lifshitz-Baryakhtar equation, J. Diff. Eqs., 2023, 371, 191–230. doi: 10.1016/j.jde.2023.06.033 CrossRef Google Scholar
[16]	M. Tilioua, On a phase transition model in ferromagnetism, Appl. Math. Model., 2010, 34(12), 3943–3948. doi: 10.1016/j.apm.2010.03.030 CrossRef Google Scholar