The present paper elustrates the global theory of deep cellular growth in directional solidification. Especially the paper demonstrates the following issues: the multiple structure of steady state solutions, the presence of simle turning point singularty in the root region, the  mechanism interface-closure; the global stabilities of the system and selection of steady states, the essence of the side-branching structure formed in oscillatory cellular growth.

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1. global theory of deep cellular growth in directional solidification
2. Global theory for steady lamellar eutectic growth in directional solidification
3. Global stabilities and selection of lamellar eutectic growth in directional solidifation
4. Global stabilities and selection of steady lamellar eutectec growth in directional solidification.