Existence and Uniqueness of Weak Solutions for a Class of Viscous Diffusion Equations

QU Chengyuan; WEI Xiaodan

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Existence and Uniqueness of Weak Solutions for a Class of Viscous Diffusion Equations

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- Existence and Uniqueness of Weak Solutions for a Class of Viscous Diffusion Equations
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 53, Issue 3, Pages: 57-60(2014)
- 作者机构：
  
  1. 大连民族学院理学院,辽宁,大连,116600
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2014，
  
  Published Online：25 May 2014，
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QU Chengyuan, WEI Xiaodan. Existence and Uniqueness of Weak Solutions for a Class of Viscous Diffusion Equations. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(3):57-60(2014)
DOI：

QU Chengyuan, WEI Xiaodan. Existence and Uniqueness of Weak Solutions for a Class of Viscous Diffusion Equations. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(3):57-60(2014) DOI：

摘要

主要考虑一类粘性扩散方程(∂u / ∂t－λ ∂Δu / ∂t－div(g( | ▽G

* u |)▽u)=0的Neumann边值问题。此类方程也称为伪抛物型方程，它具有丰富的物理背景，在土壤力学、热传导及流体力学中有着广泛的应用，与图像恢复也有着密切联系。主要利用不动点方法证明其弱解的存在性

进一步证明弱解的唯一性。

Abstract

The Neumann problem of a class of viscous diffusion equation (∂u / ∂t－λ ∂Δu / ∂t－div(g( | ▽G

* u |)▽u)=0 is studied. Such equation is also called pseudo-parabolic equation

which has a rich physics background

and has a wide range of applications in soil mechanics

heat transfer and fluid mechanics

and also is closely related with image restoration. Using the fixed point method

the existence of weak solutions is proved

and the uniqueness of the solution is obtained.

关键词

粘性扩散方程弱解存在性唯一性

Keywords

viscous diffusion equationweak solutionexistenceuniqueness

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Related Author

WANG Qiru

CHENG Shihui

GAO Jin

盛立人

箭

肖

宋国强

YAN Xiaoli

Related Institution

．School of Mathematics and Computational Science, Sun Yatsen University

．Department of Information Technology, Henan Institute of Education

College of Health Administration, Anhui Medical University

College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics

Department of Mathematics, Liupanshui Normal College

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