耦合线性复Ginzburg-Landau方程组的不灵敏控制和反问题

发布时间：2018-05-07 17:12

本文选题：不灵敏控制 + 反问题　；参考：《东北师范大学》2017年硕士论文

【摘要】：本篇学位论文主要研究了耦合线性复Ginzburg-Landau方程组的不灵敏控制和一类反问题.采用的研究方法是Carleman估计.不灵敏控制的作用是当初始测量具有小误差时,保证系统的能量几乎不发生改变,即用于去除系统关于外部干扰的敏感性.为建立耦合线性复Ginzburg-Landau方程组不灵敏控制的存在性,本文将其转化为由两个正向以及两个倒向复Ginzburg-Landau方程构成的耦合系统在单个控制下的能控性问题.已有的不灵敏控制结果主要是对于单个的发展方程建立的.在已有的耦合实值抛物型方程组的不灵敏结果中,能量仅与一个解分量有关.本文研究了一类复值的耦合抛物系统,能量与所有解分量都相关.利用不动点方法,本篇论文的结果可以推广到一般的非线性复值耦合系统.另一方面,本文还建立了耦合线性复Ginzburg-Landau方程组的一类逆时间问题.在常系数情形,给出了观测不等式成立的系数刻画.同时,还得到了耦合系统的倒向唯一性和一类条件稳定性结果.
[Abstract]:In this dissertation, insensitive control and a class of inverse problems for coupled linear complex Ginzburg-Landau equations are studied. The research method used is Carleman estimation. The effect of insensitive control is to ensure that the energy of the system is almost unchanged when the initial measurement has a small error, that is, to remove the sensitivity of the system to external interference. In order to establish the existence of insensitive control for coupled linear complex Ginzburg-Landau equations, this paper transforms it into the controllability of coupled systems composed of two forward and two backward complex Ginzburg-Landau equations under a single control. The existing insensitive control results are mainly established for a single evolution equation. In the insensitive results of coupled real valued parabolic equations, the energy is related to only one solution component. In this paper, we study a class of coupled parabolic systems with complex values. The energy is correlated with all solution components. By using the fixed point method, the results of this paper can be extended to general nonlinear complex coupled systems. On the other hand, we also establish a class of inverse time problems for coupled linear complex Ginzburg-Landau equations. In the case of constant coefficients, the coefficient characterization of the observational inequality is given. At the same time, the backward uniqueness of coupled systems and a class of conditional stability results are obtained.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231;O175

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