2024/12/04 by Mchedlov-Petrosyan, P. O., Л. Н. Давыдов, Davydov, L. N. +2
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2412.03156
openalex publication_date 2024/12/04 · openalex created_date 2024/12/06 · openalex updated_date 2026/07/28
To describe highly heterogeneous systems using the Cahn-Hilliard equation, the standard form of the thermodynamic potential with a constant coefficient in the gradient term and a polynomial of the fourth degree may not be sufficient. The modification of the form of the thermodynamic potential with a polynomial of the sixth degree and the quadratic dependence of the coefficient at the gradient term is considered. Exact solutions in the form of a moving static wave and the conditions of their existence depending on the symmetry of the potential are obtained.