The present paper is concerned with the stability and selection of  the steady eutectic growth in directional solidification of binary mixtures. We performed the global asymptotic analysis in the limit of Peclet number ε approacheds to zero, and derived that the system involves two types of global instabilities: the low frequency (LF) instability and the global oscillatory wave (OW) instability. These instability mechanisms determine the selection of the steady state and eutectic pattern formation of the system.

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