The present paper is concerned with the global stability mechanisms of the steady state of lamellar eutectic  growth in directional solidification, which depends on two free parameters the Peclect number ε and the tilted angle φ.

   We perform the asymptotic analysis in the limit of Peclet number ε→0 and the  segregation coefficient parameter κ→1 and find that the system involves two types of global instabilities: the low frequency (LF) instability and the oscillatory wave (OS) instabilities.  Each of these stability mechanisms may have two types of modes,  symmetric (S)-modes and anti-symmetric (A)-modes. The neutral LF modes yield the steady interface-patterns, while the neutral oscillatory wave modes yield the oscillatory interface-patterns. It appears that similar to the case of deep cellular growth, there is no selection in eutectic growth, neither for the steady state,  nor for the oscillatory state.  The neutral curves of these two types of global instability mechanisms on(φ,ε) -plane have the intersection, which determines the transition of the steady periodic pattern to the oscillatory pattern.

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4. Global stabilities and selection of steady lamellar eutectec growth in directional solidification.