Bifurcations of steady states for the Eguchi–Oki–Matsumura model of phase separation

Abstract

This article is concerned with bifurcations of steady states for a model system of phase separation, which is introduced by Eguchi–Oki–Matsumura (EOM). The system consists of coupled two evolution equations and admits steady state solutions with different energies. The bifurcation phenomena of these steady states with respect to the principal parameter, which is related to the temperature, are analyzed.

Keywords:

• Phase separation
• Eguchi–Oki–Matsumura model
• Steady state solution
• Bifurcation analysis

Keywords:

• 2000 Mathematics Subject Classifications: 80A30
• 37C75
• 35K45

Acknowledgments

The authors are grateful to the referee for various suggestions, which helped in improving the manuscript. This work is partially supported by Grants-in-Aids for Scientific Research (No. 16540184), from the Japan Society for Promotion of Sciences.