Author: Costica Morosanu

Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods

Personal Book: US $49 Special Offer (PDF + Printed Copy): US $191
Printed Copy: US $167
Library Book: US $196
ISBN: 978-1-60805-647-7
eISBN: 978-1-60805-350-6 (Online)
Year of Publication: 2012
DOI: 10.2174/97816080535061120101

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.

Indexed in: Book Citation Index, Science Edition, Scopus, EBSCO.

Foreword

This book is concerned with the analysis and optimal control of the phase-field transition mathematical model described by Caginalp phase-field parabolic system, which was proposed in 1986 to replace the classical two-phase Stephan problem. With respect to the Stephan free boundary model of phase transition, the Caginalp model describes better and more accurately the physical processes of melting and solidification and is now widely accepted in mathematical physics. It is also a more convenient way to represent the moving boundary of melting and solidification processes.

From mathematical point of view, the great advantage is that the new model is represented by a parabolic semilinear system with a nonlinearity of Ginzburg-Landau type, while the classical Stephan model is described by a parabolic variational inequality, which is a parabolic multivalued equation hardly to solve or approximate.

In this book the author, who has several important contributions in theory of otimal control problems of phase-field systems, has rigorously presented the existence and approximation theory of this phase-field system as well as the theory of otimal control problems governed by this system. Applications to control of solidification region in specific industrial processes and numerical tests are also included. Most of the results presented in this book are new or taken from author’s previous works. It is in our opinion a good and useful work for all pure and applied mathematicians interested in phase transition mathematical models.

Viorel BARBU
University ”Al. I. Cuza” and
Romanian Academy


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