树状网络上一维非线性双曲守恒律系统的能控性

项目名称： 树状网络上一维非线性双曲守恒律系统的能控性

项目编号： No.11526050

项目类型： 专项基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 王珂

作者单位： 东华大学

项目金额： 3万元

中文摘要： 非线性双曲守恒律系统具有很强的实际应用背景，被广泛应用于动力学、生物学、医学以及工业生产等各个领域。研究由这类系统支配的流体动力学模型的控制问题，是近代数学中一个备受关注的前沿研究方向。但由于对双曲守恒律系统的熵解在理论分析上有很大的难度，且实际问题往往具有很大的复杂性和多样性，研究这类系统的控制问题在数学上是一个重大的挑战，而在网络上研究这一类问题则具有更大的难度。本课题主要研究非线性双曲守恒律系统在两个具有很强实际背景的网络模型中的应用，研究其相关的能控性问题，为解决相应的实际问题提供理论依据及指导。

中文关键词： 双曲型方程(组)；非线性双曲守恒律系统；能控性；能观性；树状网络

英文摘要： Nonlinear hyperbolic systems of conservation laws have strong practical background, they are widely applied on dynamics, biology, medicine, industry, etc.. The associated research on control problems for this kind of systems is a forward direction in modern mathematics, and is attracting more and more attentions. However, due to the difficulty in theoretical analysis on hyperbolic systems of conservation laws in the framework of entropy solutions, as well as the complexity and variety in reality, it is a big challenge to study control problems for such systems in the context of entropy solutions. Moreover, it is more difficult and more complicated to consider these problems on networks. This proposal is mainly concerned with two models arising from reality, and we are mainly interested in controllability for related hyperbolic systems of conservation laws on networks. These results would provide theoretical foundation and guidance for solving related reality problems.

英文关键词： Hyperbolic Systems；Nonlinear Hyperbolic Systems of Conservation Laws；Controllability；Observability；Tree-like Networks