Error estimate of the finite volume scheme for the Allen–Cahn equation
Sign Up to like & getrecommendations! Published in 2018 at "BIT Numerical Mathematics"
DOI: 10.1007/s10543-017-0687-4
Abstract: The Allen–Cahn equation originates in the phase field formulation of phase transition phenomena. It is a reaction-diffusion ODE with a nonlinear reaction term which allows the formation of a diffuse phase interface. We first introduce… read more here.
Keywords: cahn equation; finite volume; scheme; allen cahn ... See more keywords
A practical adaptive grid method for the Allen–Cahn equation
Sign Up to like & getrecommendations! Published in 2021 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2021.125975
Abstract: Abstract We present a simple and practical adaptive finite difference method for the Allen–Cahn (AC) equation in the two-dimensional space. We use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain.… read more here.
Keywords: practical adaptive; cahn equation; method; equation ... See more keywords
Entire solutions originating from monotone fronts to the Allen–Cahn equation
Sign Up to like & getrecommendations! Published in 2018 at "Physica D: Nonlinear Phenomena"
DOI: 10.1016/j.physd.2018.04.003
Abstract: Abstract In this paper, we study entire solutions of the Allen–Cahn equation in one-dimensional Euclidean space. This equation is a scalar reaction–diffusion equation with a bistable nonlinearity. It is well-known that this equation admits three… read more here.
Keywords: originating monotone; cahn equation; solutions originating; allen cahn ... See more keywords
The stability of the equilibria of the Allen–Cahn equation with fractional diffusion
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2017.1399360
Abstract: ABSTRACT This paper is mainly concerned with the stability of the equilibria of the Allen–Cahn equation where the standard Laplacian diffusion is replaced by the fractional Laplacian diffusion. We shall show that the state is… read more here.
Keywords: diffusion; cahn equation; stability equilibria; equilibria allen ... See more keywords
An Energy Minimization-Based Deep Learning Approach with Enhanced Stability for the Allen-Cahn Equation
Sign Up to like & getrecommendations! Published in 2025 at "Axioms"
DOI: 10.3390/axioms14110806
Abstract: The Allen-Cahn equation is a fundamental model in materials science for describing phase separation phenomena. This paper introduces an Energy-Stabilized Scaled Deep Neural Network (ES-ScaDNN) framework to solve the Allen-Cahn equation by energy minimization. Unlike… read more here.
Keywords: allen cahn; cahn equation; energy minimization;
Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions
Sign Up to like & getrecommendations! Published in 2017 at "Evolution Equations and Control Theory"
DOI: 10.3934/eect.2017012
Abstract: In this paper, we discuss the existence of the periodic solutions of a Cahn-Hillard/Allen-Cahn equation which is introduced as a simplification of multiple microscopic mechanisms model in cluster interface evolution. Based on the Schauder type… read more here.
Keywords: space; cahn equation; space dimensions; allen cahn ... See more keywords