A Qualitative Analysis of a Nonlinear Second-Order Anisotropic Diffusion Problem with Non-homogeneous Cauchy-Stefan-Boltzmann Boundary Conditions

被引：15

作者：

Miranville, Alain ^{[1
,2
]}

Morosanu, Costica ^{[3
]}

机构：

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

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

[3] Alexandru Ioan Cuza Univ, Fac Math, Bd Carol I,11, Iasi 700506, Romania

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2021年 / 84卷 / 01期

关键词：

Nonlinear anisotropic diffusion; Qualitative properties of solutions; Leray-Schauder principle; FIELD TRANSITION SYSTEM; GENERAL-CLASS; PHASE; EXISTENCE; REGULARITY; UNIQUENESS; NEUMANN; MODEL;

D O I：

10.1007/s00245-019-09643-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper is concerned with a qualitative analysis for a nonlinear second-order parabolic problem, subject to non-homogeneous Cauchy-Stefan-Boltzmann boundary conditions, extending the types already studied. Under certain assumptions, we prove the existence, a priori estimates, regularity and uniqueness of a solution in the class W-p(1,2) ( Q). Here we extend the results already proven by the authors for a nonlinearity of cubic type, making the present mathematical model to be more capable for describing the complexity of certain wide classes of real physical phenomena (phase separation and transition, for instance).

引用

页码：227 / 244

页数：18

共 37 条

[31] On the Convergence of an Approximation Scheme of Fractional-Step Type, Associated to a Nonlinear Second-Order System with Coupled In-Homogeneous Dynamic Boundary Conditions
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[32] ANALYSIS OF AN ITERATIVE SCHEME OF FRACTIONAL STEPS TYPE ASSOCIATED TO THE NONLINEAR PHASE-FIELD EQUATION WITH NON-HOMOGENEOUS DYNAMIC BOUNDARY CONDITIONS
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[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2024,
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[J]. VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2016, 20 (03): : 389 - 409
[36] System of Nonlinear Second-Order Parabolic Partial Differential Equations with Interconnected Obstacles and Oblique Derivative Boundary Conditions on Non-Smooth Time-Dependent Domains
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[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2023, 88 (02):
[37] System of Nonlinear Second-Order Parabolic Partial Differential Equations with Interconnected Obstacles and Oblique Derivative Boundary Conditions on Non-Smooth Time-Dependent Domains
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