On a class of sixth order viscous Cahn-Hilliard type equations
type: Item
instance of: scholarly article
title: On a class of sixth order viscous Cahn-Hilliard type equations
zbMATH Open document ID: 1276.35100
author: Wojciech M. Zajączkowski
author: I. Pawłow
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2013-03-14T00:00:00Z
review text: An initial boundary value problem for a class of sixth order viscous Cahn-Hilliard type equations with nonlinear diffusion is considered. Such type problem arises in phase-field modeling of various spatial structures, for example in oil-water-surfactant mixtures and modeling of crystal growth on atomic length, known as phase field cristal model. It is proved existence and uniqueness of a global in time regular solution. By means of the Leray-Schauder fixed point theorem the finite time existence is proved. Based on suitable estimates of solutions, the finite time solution is extended step by step on the infinite time interval.
reviewed by: Mersaid Aripov
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35K58
zbMATH DE Number: 6144730
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: oil-water-surfactant mixtures
zbMATH Keywords: Leray-Schauder fixed point theorem
MaRDI profile type: Publication
full work available at URL: dcdss.2013.6.517
OpenAlex ID: W2327594184
DOI: 10.3934/DCDSS.2013.6.517
description: scientific article; zbMATH DE number 6144730