| 椭圆-抛物方程描述液体-固体的相互作用 |
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| 引用本文： | 宗西举,赵怡,周毅,曾丽.椭圆-抛物方程描述液体-固体的相互作用[J].中山大学学报(自然科学版),2007,46(3):1-4,13. |
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| 作者姓名： | 宗西举 赵怡 周毅 曾丽 |
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| 作者单位： | 中山大学数学与计算科学学院 广东广州510275(宗西举，赵怡)，中山大学基础医学院生物医学工程系 广东广州510080(周毅)，广东外语外贸大学信息学院应用数学系 广东广州510420(曾丽) |
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| 摘 要： | 讨论一维液体-固体相互作用的简单模型。波在液体中传播,满足一维椭圆-抛物型方程。液体中漂浮着一质点固体,固体在波的传播的影响下随波漂流,固体的速度和它所在的位置处的波的传播速度相同。利用Banach不动点原理和算子半群理论得到这一液体-固体相互作用的系统的解是整体存在、唯一的。而且,利用能量估计,得到系统的解的长时间性态,以及在质点固体两侧液体对它的压力渐近消失。
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| 关 键 词： | 一维椭圆-抛物型方程 液体-固体相互作用 Banach不动点原理 能量估计 |
| 文章编号： | 0529-6579（2007）03-0001-05 |
| 修稿时间： | 2006-08-17 |
Large Time Behavior for a Simplified 1-D Parabolic- Elliptic Model of Fluid-Solid Interaction |
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| ZONG Xi-ju,ZHAO Yi,ZHOU Yi,ZENG Li.Large Time Behavior for a Simplified 1-D Parabolic- Elliptic Model of Fluid-Solid Interaction[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2007,46(3):1-4,13. |
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| Authors: | ZONG Xi-ju ZHAO Yi ZHOU Yi ZENG Li |
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| Institution: | 1. School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China; 2. Department of Biomedical Engineering, School of Basic Medical Science, Sun Yat-sen University, Guangzhou 510080, China 3. Department of Applied Mathematics, School of Informatics,Guangdong University of Foreign Studies, Guangzhou 510420, China |
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| Abstract: | A simple model in one space dimension for the interaction between a fluid and a solid represented by a point mass is considered.The fluid is governed by the parabolic-elliptic equation and the solid mass,which shares the velocity of the fluid,is accelerated by the difference of pressure at both sides of it.By using semi-group theorem and Banach fixed-point theorem,the existence and uniqueness of the solution to the system is obtained.Furthermore,the asymptotic behavior of solutions for integrable data is described by using energy estimates.Asymptotically,the difference of pressure to both sides of the point mass vanishes are also proved. |
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| Keywords: | fluid-solid interaction one-dimension parabolic-elliptic equation large time behavior Banach fixed-point theorem energy estimate |
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