非线性热动力系统在Neumann边界控制下的整体解

项目名称： 非线性热动力系统在Neumann边界控制下的整体解

项目编号： No.61473180

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 丁俊堂

作者单位： 山西大学

项目金额： 80万元

中文摘要： 非线性热动力系统的整体解和爆破解分别描述了系统的稳定状态和不稳定状态。在安全地利用核能发电和金属冶炼的安全生产等很多重要的实际问题中，我们需要热动力系统处于稳定状态，然而如果对这些系统不加以控制，系统就可能会处于不稳定状态。热动力系统在不稳定状态下运行就会导致灾难性的安全事故的发生。本项目的研究主要是通过对非线性热动力系统设计Neumann边界控制，使系统从不稳定状态转变为稳定状态，也就是通过对系统设计Neumann边界控制来消除系统中的爆破解。到目前为止国内外学者在这方面的研究主要集中在半线性热动力系统，而对于热源项、传导项和扩散项都是非线性的热动力系统研究不多成果较少。本项目是申请者多年来基于对非线性反应扩散动力系统在边界控制下的整体解和爆破解研究的基础上提出来的新课题，这也是分布参数系统控制理论研究的一个新课题，项目的研究成果在核能发电和金属冶炼等许多领域有非常重要的理论和应用价值。

中文关键词： 非线性；热动力系统；边界控制；整体解

英文摘要： The global and blow-up of solutions for nonlinear heat dynamical system describe the stable state and unstable state of the system, respectively. In many important practical problems,such as using safely unclear energy to generate electricity and safe production of metals smelting, we hope the heat dynamical systems to be stable. However, if we do not control these heat dynamical systems, the systems are usually unstable. The operation of heat power system in an unstable state will lead to the occurrence of catastrophic safety accidents.In this plan, our strategy is that by designing the Neumann boundary control for nonlinear heat dynamical system, we can transmit the system from the unstable state into stable state. In other words, by designing the Neumann boundary control, we can eliminate the blow-up solution of nonlinear heat dynamical system. Up to now, the scholars at home and abroad study mainly semilinear heat dynamical systems. So far as I know, there are a few results being made to the nonlinear heat dynamical systems in which heat source, convection and diffusion are all nonlinear. This plan is a new project rasied by the applicant on the basis of the study in these years about the global and blow-up solutions for nonlinear reaction diffusion dynamical system under boundary control. This plan on the global solution of nonlinear heat dynamical system under Neumann boundary control is a new study area of distributed parameter control theory. Our study results have important theoretical and applied value in many fields such as nuclear power generation and metals smelting.

英文关键词： nonlinear;heat dynamical system;boundary control;global solution