ON THE LOGARITHMIC CAHN-HILLIARD EQUATION WITH GENERAL PROLIFERATION TERM

被引：0

作者：

Mheich, Rim ^{[1
,3
]}

Petcu, Madalina ^{[1
]}

Talhouk, Raafat ^{[2
,3
]}

机构：

[1] Univ Poitiers, Lab Math & Applicat, Chasseneuil, France

[2] Leonard de Vinci Pole Univ, Res Ctr, F-92916 Paris, France

[3] Univ Libanaise, EDST, Lab Math, Hadath, Lebanon

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2024年 / 23卷 / 03期

关键词：

Cahn-Hilliard Equation; well-posedness; logarithmic nonlinear term; existence; regularization term; regular nonlinear term; attractors; strict separation property; Dirichlet boundary conditions; finite-dimensional attractors; numerical simulations; FE-CR ALLOYS; SPINODAL DECOMPOSITION; COMPUTER-MODELS; ATOMIC-LEVEL; EXPONENTIAL ATTRACTORS; HIGHER DIMENSIONS;

D O I：

10.3934/cpaa.2024016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim in this article is to study the well-posedness of the generalized logarithmic nonlinear Cahn-Hilliard equation with regularization and proliferation terms. We are interested in studying the asymptotic behavior, in terms of finite-dimensional attractors, of the dynamical system associated with the problem and majorate the rate of convergence between the solutions of the Cahn-Hilliard equation and the regularized one. Additionally, we present some further regularity results and subsequently prove a strict separation property of the solution. Finally, we provide some numerical simulations to compare the solution with and without the regularization term, and more.

引用

页码：383 / 403

页数：21

共 50 条

[31] SPINODAL DECOMPOSITION FOR THE CAHN-HILLIARD EQUATION
GRANT, CP
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (3-4) : 453 - 490
[32] Local Dynamics of Cahn-Hilliard Equation
Kashchenko, S. A.
Plyshevskaya, S. P.
[J]. NONLINEAR PHENOMENA IN COMPLEX SYSTEMS, 2019, 22 (01): : 93 - 97
[33] NONLINEAR ASPECTS OF THE CAHN-HILLIARD EQUATION
NOVICKCOHEN, A
SEGEL, LA
[J]. PHYSICA D, 1984, 10 (03): : 277 - 298
[34] ENERGY METHODS FOR THE CAHN-HILLIARD EQUATION
NOVICKCOHEN, A
[J]. QUARTERLY OF APPLIED MATHEMATICS, 1988, 46 (04) : 681 - 690
[35] Existence of solution to a Cahn-Hilliard equation
Mourad, Ayman
Taha, Zahraa
[J]. ASYMPTOTIC ANALYSIS, 2022, 130 (3-4) : 387 - 408
[36] Attractors for some models of the Cahn-Hilliard equation with the inertial term
Khanmamedov, Azer
[J]. NONLINEARITY, 2023, 36 (02) : 1120 - 1142
[37] On the 2D Cahn-Hilliard Equation with Inertial Term
Grasselli, Maurizio
Schimperna, Giulio
Zelik, Sergey
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (02) : 137 - 170
[38] A nonlocal stochastic Cahn-Hilliard equation
Cornalba, Federico
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 140 : 38 - 60
[39] Convergence of solutions to Cahn-Hilliard equation
Rybka, P
Hoffmann, KH
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (5-6) : 1055 - 1077
[40] Some generalizations of the Cahn-Hilliard equation
Miranville, A
[J]. ASYMPTOTIC ANALYSIS, 2000, 22 (3-4) : 235 - 259

← 1 2 3 4 5 →