Asymptotic solution of cellular growth in directional solidification

The present thesis is concerned with steady state of cellular growth in directional solidification with a small Peclet number and isotropic surface tension. A uniformly valid asymptotic expansion solution is obtained by applying the MVE (Multiple Variables Expansion) method. The results of the present thesis show that this system allows a continuous family of steady state solutions with a undetermined, interfacial stability parameter epsilon and a discrete quantization number n. Not all these solutions are observable in the experiments, so the selection problem remains