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| 一类粘性扩散方程弱解的存在唯一性 | |
| 引用本文： | 曲程远,魏晓丹. 一类粘性扩散方程弱解的存在唯一性[J]. 中山大学学报(自然科学版), 2014, 53(3): 57-60,66 |
| 作者姓名： | 曲程远 魏晓丹 |
| 作者单位： | 1.大连民族学院理学院，辽宁 大连 116600； 2.大连民族学院计算机科学与工程学院，辽宁 大连 116600 |
| 基金项目： | 国家自然科学基金资助项目(11226179) |
| 摘 要： | 主要考虑一类粘性扩散方程u/t-λΔu/t-div(g(|▽Gσ*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。 |
| 关 键 词： | 粘性扩散方程 弱解 存在性 唯一性 |
| 收稿时间： | 2014-02-22; |
Existence and Uniqueness of Weak Solutions for a Class of Viscous Diffusion Equations |
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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, 2014, 53(3): 57-60,66 | |
| Authors: | QU Chengyuan WEI Xiaodan |
| Affiliation: | 1. Department of Mathematics, Dalian Nationalities University, Dalian 116600, China; 2. College of Computer Science & Technology, Dalian Nationalities University, Dalian 116600, China |
| Abstract: | The Neumann problem of a class of viscous diffusion equation (∂u / ∂t－λ ∂Δu / ∂t－div(g( | ▽Gσ * 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. |
| Keywords: | viscous diffusion equation；weak solution；existence uniqueness |
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