本文選題：不靈敏控制 + 反問題　； 參考：《東北師范大學(xué)》2017年碩士論文

【摘要】：本篇學(xué)位論文主要研究了耦合線性復(fù)Ginzburg-Landau方程組的不靈敏控制和一類反問題.采用的研究方法是Carleman估計.不靈敏控制的作用是當(dāng)初始測量具有小誤差時,保證系統(tǒng)的能量幾乎不發(fā)生改變,即用于去除系統(tǒng)關(guān)于外部干擾的敏感性.為建立耦合線性復(fù)Ginzburg-Landau方程組不靈敏控制的存在性,本文將其轉(zhuǎn)化為由兩個正向以及兩個倒向復(fù)Ginzburg-Landau方程構(gòu)成的耦合系統(tǒng)在單個控制下的能控性問題.已有的不靈敏控制結(jié)果主要是對于單個的發(fā)展方程建立的.在已有的耦合實值拋物型方程組的不靈敏結(jié)果中,能量僅與一個解分量有關(guān).本文研究了一類復(fù)值的耦合拋物系統(tǒng),能量與所有解分量都相關(guān).利用不動點方法,本篇論文的結(jié)果可以推廣到一般的非線性復(fù)值耦合系統(tǒng).另一方面,本文還建立了耦合線性復(fù)Ginzburg-Landau方程組的一類逆時間問題.在常系數(shù)情形,給出了觀測不等式成立的系數(shù)刻畫.同時,還得到了耦合系統(tǒng)的倒向唯一性和一類條件穩(wěn)定性結(jié)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.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O231;O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 ZHANG MuMing;LIU Xu;;Insensitizing controls for a class of nonlinear Ginzburg-Landau equations[J];Science China(Mathematics);2014年12期

2 ;Attractors for the Ginzburg-Landau-BBME quations in an Unbounded Domain[J];Communications in Nonlinear Science & Numerical Simulation;1998年02期

，

本文編號：1857762