5 papers · 1 filter
The -Limit Problem: Convergence of a Linear Degenerate Interface Transmission Problem
Toai Luong, Tadele Mengesha, Kerrek Stinson +2
We study the singular limit of a family of linear degenerate interface transmission problems arising from a regularization procedure in the newly proposed Two-Parameter Diffuse Dom…
A Diffuse Domain Approximation with Transmission-Type Boundary Conditions II: Gamma--Convergence
Toai Luong, Tadele Mengesha, Steven M. Wise +1
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by rep…
A Diffuse Domain Approximation with Transmission-Type Boundary Conditions I: Asymptotic Analysis and Numerics
Toai Luong, Tadele Mengesha, Steven M. Wise +1
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly repr…
A Nonnegative Weak Solution to the Phase Field Crystal Model with Degenerate Mobility
Toai Luong, Steve Wise
Phase field crystal is a model used to describe the behavior of crystalline materials at the mesoscale. In this study, we investigate the well-posedness of a phase field crystal eq…
Nonnegative Weak Solution to the Degenerate Viscous Cahn-Hilliard Equation
Toai Luong
The Cahn-Hilliard equation is a widely used model for describing phase separation processes in a binary mixture. In this paper, we investigate the viscous Cahn-Hilliard equation wi…