ANALYSIS OF AN ITERATIVE SCHEME OF FRACTIONAL STEPS TYPE ASSOCIATED TO THE NONLINEAR PHASE-FIELD EQUATION WITH NON-HOMOGENEOUS DYNAMIC BOUNDARY CONDITIONS

被引：11

作者：

Miranville, Alain ^{[1
]}

Morosanu, Costica ^{[2
]}

机构：

[1] Univ Poitiers, Lab Math & Applicat, UMR CNRS 7348, SP2MI, F-86962 Futuroscope, France

[2] Alexandru Ioan Cuza Univ, Iasi 700506, Romania

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2016年 / 9卷 / 02期

关键词：

Boundary value problems for nonlinear parabolic PDE; stability and convergence of numerical methods; nonhomogeneous dynamic boundary conditions; thermodynamics; heat transfer; ALLEN-CAHN EQUATION; LONG-TIME BEHAVIOR; TRANSITION SYSTEM; EXPONENTIAL ATTRACTORS; SINGULAR POTENTIALS; CAUCHY-NEUMANN; MODEL; APPROXIMATION; EXISTENCE;

D O I：

10.3934/dcdss.2016011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper concerns with the existence, uniqueness, regularity and the approximation of solutions to the nonlinear phase-field (Allen-Cahn) equation, endowed with non-homogeneous dynamic boundary conditions (depending both on time and space variables). It extends the already studied types of boundary conditions, which makes the problem to be more able to describe many important phenomena of two-phase systems, in particular, the interactions with the walls in confined systems. The convergence and error estimate results for an iterative scheme of fractional steps type, associated to the nonlinear parabolic equation, are also established. The advantage of such method consists in simplifying the numerical computation. On the basis of this approach, a conceptual numerical algorithm is formulated in the end.

引用

页码：537 / 556

页数：20

共 23 条

[1] Fractional Steps Scheme to Approximate the Phase-Field Transition System with Non-Homogeneous Cauchy-Neumann Boundary Conditions
Benincasa, T.
Morosanu, C.
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2009, 30 (3-4) : 199 - 213
[2] On the existence, uniqueness and regularity of solutions to the phase-field transition system with non-homogeneous Cauchy-Neumann and nonlinear dynamic boundary conditions
Miranville, Alain
Morosanu, Costica
[J]. APPLIED MATHEMATICAL MODELLING, 2016, 40 (01) : 192 - 207
[3] NUMERICAL APPROXIMATION OF THE PHASE-FIELD TRANSITION SYSTEM WITH NON-HOMOGENEOUS CAUCHY-NEUMANN BOUNDARY CONDITIONS IN BOTH UNKNOWN FUNCTIONS VIA FRACTIONAL STEPS METHOD
Ovono, Armel Andami
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2013, 3 (04): : 377 - 397
[4] Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions
Cabada, Alberto
Wanassi, Om Kalthoum
[J]. MATHEMATICS, 2020, 8 (02)
[5] Analysis of an iterative scheme of fractional steps type associated to the reaction-diffusion equation endowed with a general nonlinearity and Cauchy-Neumann boundary conditions
Morosanu, Costica
Croitoru, Anca
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 425 (02) : 1225 - 1239
[6] Phase-field systems with nonlinear coupling and dynamic boundary conditions
Cavaterra, Cecilia
Gal, Ciprian G.
Grasselli, Maurizio
Miranville, Alain
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (05) : 2375 - 2399
[7] On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions
Carja, Ovidiu
Miranville, Alain
Morosanu, Costica
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 113 : 190 - 208
[8] The phase-field transition system with non-homogeneous Cauchy-Stefan-Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity
Morosanu, Costica
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 87 : 22 - 32
[9] Optimal control problem for phase-field equations with nonlinear dynamic boundary conditions
Aiki, T
Kadoya, A
Sato, N
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (05) : 3183 - 3194
[10] STABILITY AND ERRORS ANALYSIS OF TWO ITERATIVE SCHEMES OF FRACTIONAL STEPS TYPE ASSOCIATED TO A NONLINEAR REACTION-DIFFUSION EQUATION
Morosanu, Costica
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2020, 13 (05): : 1567 - 1587

← 1 2 3 →