Introduction

All developments in mathematics and computer science facilitate development of industrial applications. This e-book approaches the subject in a profoundly interdisciplinary manner. The spectrum of subjects covered in this e-book includes mathematics, computer science, materials science and industrial applications. Specifically, the e-book elaborates on mathematical models of phase-field transitions. Nonlinear parabolic systems represent the core of this book.

Mathematically speaking, it presents methods related to existence, uniqueness and regularity of solution, fractional steps, analysis of some boundary optimal control problems governed by phase-field transition system, conceptual algorithms to compute the approximate solution and boundary control.

Aspects of computer implementation of algorithms and numerical results obtained through their use are also included. This volume should be a valuable reference for software engineers interested in modeling and simulation of phase transition processes.