Higher order potential in the modified convective-viscous Cahn-Hilliard equation
Abstract
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.
Cite
@article{arxiv.2412.03156,
title = {Higher order potential in the modified convective-viscous Cahn-Hilliard equation},
author = {P. O. Mchedlov-Petrosyan and L. N. Davydov and O. A. Osmaev},
journal= {arXiv preprint arXiv:2412.03156},
year = {2025}
}
Comments
9 pages, 0 figures; Latex, 10 pages; corrected spelling of an author name (translated from Cyrillic), corrected technical mistakes, essentially extended discussion in section 4, results unchanged