In this presentation we shall, by using analytical approach, elucidate the following issues concerned with the global feature of deel cellular growth: the multi-layer structure of the steady state, mechenism of the interface-closure in the root region; the global stabilities and selection of pattern formation. 

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1. Global theory for steady lamellar eutectic growth in directional solidification
2. The global theory of deep cellular growth in direcional 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.