ANALYSIS AND OPTIMAL CONTROL OF PHASE-FIELD TRANSITION SYSTEM

Abstract

In the present paper we prove same new existence results of solutions for phase-field model subject to different types of boundary conditions. The methods used here are especially based on the Leray-Schauder degree, on same estimates and on elliptic regularity of corresponding weak solution. We also establish several results of convergence for iterative schemes of fractional steps type associated to phase-field model. The main tools used in the proof are the compactness methods and the Lie-Trotter product formula.