Analysis for Allen-Cahn-Ohta-Nakazawa Model in a Ternary System
Sookyung Joo, Xiang Xu, Yanxiang Zhao
TL;DR
This paper investigates the mathematical properties of the Allen-Cahn Ohta-Nakazawa model in a ternary system, establishing well-posedness through a novel application of the gradient flow framework and De Giorgi's scheme.
Contribution
It introduces a new approach to prove existence and uniqueness of solutions for the model with volume constraints, enhancing understanding of its mathematical structure.
Findings
Proved global well-posedness of the model.
Established existence and uniqueness of solutions.
Applied a novel De Giorgi scheme for gradient flows.
Abstract
In this paper we study the global well-posedness of the Allen-Cahn Ohta-Nakazawa model with two fixed nonlinear volume constraints. Utilizing the gradient flow structure of its free energy, we prove the existence and uniqueness of the solution by following De Giorgi's minimizing movement scheme in a novel way.
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Taxonomy
TopicsSolidification and crystal growth phenomena · Nonlinear Partial Differential Equations · Navier-Stokes equation solutions