A perturbation of the Cahn-Hilliard equation with logarithmic nonlinearity

被引：4

作者：

Conti, Monica ^{[1
]}

Gatti, Stefania ^{[2
]}

Miranville, Alain ^{[3
,4
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, Via Bonardi 9, I-20133 Milan, Italy

[2] Univ Modena & Reggio Emilia, Dipartimento Sci Fis Informat & Matemat, Via Campi 213-b, I-41125 Modena, Italy

[3] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang, Henan, Peoples R China

[4] Univ Poitiers, Equipe DACTIM MIS, Lab I3M & Lab Math & Applicat, Site Futuroscope Teleport 2 11 Blvd Marie & Pierre, F-86073 Poitiers 9, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 382卷

关键词：

Cahn-Hilliard equation; Perturbation; Logarithmic nonlinear terms; Well-posedness; Strict separation property; Convergence to the Cahn-Hilliard equation; TRANSITIONS; SYSTEM;

D O I：

10.1016/j.jde.2023.11.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our aim in this paper is to study a perturbation of the Cahn-Hilliard equation with nonlinear terms of logarithmic type. This new model is based on an unconstrained theory recently proposed in [5]. We prove the existence, regularity and uniqueness of solutions, as well as (strong) separation properties of the solutions from the pure states, also in three space dimensions. We finally prove the convergence to the Cahn-Hilliard equation, on finite time intervals. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：50 / 76

页数：27

共 19 条

[1] Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy [J].

Abels, Helmut ;

Wilke, Mathias .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (11) :3176-3193

[2] ON SPINODAL DECOMPOSITION [J].

CAHN, JW .

ACTA METALLURGICA, 1961, 9 (09) :795-801

[3] FREE ENERGY OF A NONUNIFORM SYSTEM .1. INTERFACIAL FREE ENERGY [J].

CAHN, JW ;

HILLIARD, JE .

JOURNAL OF CHEMICAL PHYSICS, 1958, 28 (02) :258-267

[4] Well-posedness for the Brinkman-Cahn-Hilliard system with unmatched viscosities [J].

Conti, Monica ;

Giorgini, Andrea .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (10) :6350-6384

[5] Coupled diffusion and phase transition: Phase fields, constraints, and the Cahn-Hilliard equation [J].

Duda, Fernando P. ;

Sarmiento, Adel F. ;

Fried, Eliot .

MECCANICA, 2021, 56 (07) :1707-1725

[6]

Forest S., 2008, CONTINUUM MODELS DIS, P105

[7] A Cahn-Hilliard Model Based on Microconcentrations [J].

Forest, Samuel ;

Miranville, Alain .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (04)

[8] CONTINUUM THEORY OF THERMALLY-INDUCED PHASE-TRANSITIONS BASED ON AN ORDER-PARAMETER [J].

FRIED, E ;

GURTIN, ME .

PHYSICA D-NONLINEAR PHENOMENA, 1993, 68 (3-4) :326-343

[9] DYNAMIC SOLID-SOLID TRANSITIONS WITH PHASE CHARACTERIZED BY AN ORDER-PARAMETER [J].

FRIED, E ;

GURTIN, ME .

PHYSICA D, 1994, 72 (04) :287-308

[10] THE SEPARATION PROPERTY FOR 2D CAHN-HILLIARD EQUATIONS: LOCAL, NONLOCAL AND FRACTIONAL ENERGY CASES [J].

Gal, Ciprian G. ;

Giorgini, Andrea ;

Grasselli, Maurizio .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2023, 43 (06) :2270-2304

← 1 2 →