Abstract
A non-smooth temperature-driven phase separation model with conserved energy and a large set of equilibria is shown to develop spontaneously two different time scales as time tends to infinity. The temperature evolution becomes slower and slower, while the microevolution on the unknown phase interface keeps its own independent characteristic speed. In the large time limit, the temperature becomes uniform in space, there exists a partition of the physical body into at most three constant limit phases, and the phase separation process has a hysteresis-like character.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions. Appl. Math. Sci., Vol. 121, Springer-Verlag, New York, 1996.
P. Krejčí, Hysteresis in singularly perturbed problems. In: Singular Perturbations and Hysteresis, M. Mortell, R. O’Malley, A. Pokrovskii, V. Sobolev, eds., SIAM, Philadelphia, 2005, 73–100.
P. Krejčí and J. Sprekels, A hysteresis approach to phase-field models. Nonlin. Anal. 39 (2000), 569–586.
P. Krejčí, J. Sprekels, and S. Zheng, Asymptotic behaviour of a phase-field system with hysteresis. J. Differential Eq. 175 (2001), 88–107.
P. Krejčí and S. Zheng, Pointwise asymptotic convergence of solutions for a phase separation model, Discrete Contin. Dyn. Syst. 16 (2006), 1–18.
A. Visintin: Models of Phase Transitions. Birkhäuser, Boston, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Krejčí, P. (2006). Asymptotic Hysteresis Patterns in a Phase Separation Problem. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_28
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7719-9_28
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-7718-2
Online ISBN: 978-3-7643-7719-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)