An algebraic method for boundary control systems of parabolic type

1.线性抛物线系统的稳定性，即边界反馈的含义，已被研究。边界条件是第一类的一部分，第三类的一部分。一个非常新的和简单的代数变换（Ly D12 y D1-space中的同构）是为复杂的边界条件而引入的。通过介绍一个小型动态补偿器的通用类型，实现了更复杂的控制系统的稳定。与无边界线性运算符一起称为西尔维斯特方程的代数结构也被研究了. 2.在希尔伯特空间中研究了一个近似的无控制性问题，该问题被研究为一类线性秒顺序抛物线系统中的希尔伯特空间中的度量是如此的HUM方法。对Sine-Gordon equation的数值方法的解决方案也是根据FEM的衡量标准研究的。3.一个整体-部分差异equation已被确定为一个数学模型，用于研究人类人口与移徙的逻辑增长。这证明了Cauchy问题可以及时解决唯一的全球解决方案。“解决方案的不对称行为也是值得调查的。”该解决方案的特性已用于解释欧洲大陆最近的实验室动力学变化，4.研究了一类非线性弹性部分差异方程，其中出现的协同效应和空间域有一种对称性。解决方案的存在和独特性是通过ODE方法提供的。A generalization of the so called moving sphere method is also obtained.5.Stabilization problem is studed for linear parabolic control systems by means of HイイD1-control method。稳定的反馈控制方案的稳健性在某些拓扑中被证明是正确的。另一个稳定问题也被研究过，传感器和执行器在时间内处于周期性功能的位置。根据Brunovsky的结果（JDE， 1969年），稳定得到了实现。

1.Stabilization of linear parabolic systems by means of boundary feedback is studied. The boundary condition is partially of the first kind and partially of the third kind. An entirely new and simple algebraic transform (isomorphism in LィイD12ィエD1-spaces) is introduced for the complicated boundary condition. By introducing a finite-dimensional dynamic compensator of general type, stabilization is achieved for more complicated control systems. An algebraic structure of the so called Silvester equation with unbounded linear operators as coefficients is also studied.2.Approximate null controllability problem is studied for a class of linear second order parabolic systems in Hilbert spaces by means of the so called HUM method. A numerical approximation of solutions to the sine-Gordon equation is also studied by means of FEM.3.An integro-partial differential equation is established as a mathematical model for studing logistic growth of human population with migration. It is proven that the Cauchy problem admits the unique global solution in time. The asymptotic behavior of the solutions is also investigated. The property of solutions is used for explaining about the recent change of labor dynamics in European Continent.4.A class of nonlinear elliptic partial differential equations is studied, where the appearing coefficients and the spatial domain has a kind of symmetry. Existence and uniqueness of solutions are proven via ODE approach. A generalization of the so called moving sphere method is also obtained.5.Stabilization problem is studied for linear parabolic control systems by means of HィイD1∞ィエD1-control method. Robustness of the stabilizing feedback control scheme is proven in some topology. Another stabilization problem is also studied, where the sensors and actuators are periodic functions in time. By generalizing the result of Brunovsky (JDE, 1969), the stabilization is achieved.