On the Boussinesq-Burgers equations driven by dynamic boundary conditions

被引：7

作者：

Zhu, Neng ^{[1
,2
]}

Liu, Zhengrong ^{[1
]}

Zhao, Kun ^{[2
]}

机构：

[1] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China

[2] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Boussinesq-Burgers equations; Initial-boundary value problem; Dynamic boundary conditions; Global well-posedness; Long-time behavior; NONLINEAR DISPERSIVE MEDIA; KORTEWEG-DEVRIES EQUATION; TIME ASYMPTOTIC-BEHAVIOR; AMPLITUDE LONG WAVES; CONSERVATION-LAWS; 2-WAY PROPAGATION; GLOBAL EXISTENCE; DIFFUSION LIMIT; WATER-WAVES; SYSTEM;

D O I：

10.1016/j.jde.2017.10.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the qualitative behavior of the Boussinesq-Burgers equations on a finite interval subject to the Dirichlet type dynamic boundary conditions. Assuming H-1 x H-2 initial data which are compatible with boundary conditions and utilizing energy methods, we show that under appropriate conditions on the dynamic boundary data, there exist unique global-in-time solutions to the initial-boundary value problem, and the solutions converge to the boundary data as time goes to infinity, regardless of the magnitude of the initial data. (c) 2017 Elsevier Inc. All rights reserved.

引用

页码：2287 / 2309

页数：23

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