Approximation of The Phase Field Transition System

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 nonline...

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Bibliographic Details
Published inAnalysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods Vol. 1; no. 1; pp. 43 - 106
Main Author MOROSANU, Costica
Format Book Chapter
LanguageEnglish
Published 01.04.2012
Subjects
abstract approximation theory
nonlinear functional analysis
stability and convergence of numerical methods
nonlinear parabolic systems
semigroups of nonlinear operators
numerical analysis
fractional steps method (Lie-Trotter product formula)
operator theory
distributions
dissipative operators
degree theory
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DOI10.2174/978160805350611201010043

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Summary: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. 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...
DOI:10.2174/978160805350611201010043