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

by

Costica Morosanu

DOI: 10.2174/97816080535061120101
eISBN: 978-1-60805-350-6, 2012
ISBN: 978-1-60805-647-7



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

All developments in mathematics and computer science facilitate development of industrial applications. This e-book approaches the sub...[view complete introduction]
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Approximation of The Phase Field Transition System

- Pp. 43-106 (64)

Costica MOROSANU

Abstract

In this chapter we will deal, on one hand, with the study of the existence, uniqueness, regularity and estimates of the solution of phase-field transition system, and on the other hand, we will analyze the convergence of some approximating schemes of fractional steps type, associated to this nonlinear system. </p> <p> system. In the first Section the existence, uniqueness and regularity of the solution of the phase-field transition system subject to the non-homogeneous Cauchy-Neumann boundary conditions (Theorem 2.1) are studied. Such kind of conditions allow the phase-field system (Caginalp’s model) to be considered as a model of heat transfer from the surface of product to the environment, when we assume that heat is extracted by convection and conduction in the continuous casting process.....

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