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insensitizing controls for the Parabolic Equation with Equivalued Surface Boundary Conditions

Acta Mathematica Sinica,English Series 2012年第12期28卷 2373-2394页

作者： Zhong Qi YIN School of Mathematics Sichuan University Department of Mathematics Sichuan Normal University

This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions~ in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions.

关键词： insensitizing controls parabolic equation equivalued boundary conditions

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insensitizing controls for a class of nonlinear Ginzburg-Landau equations

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Science China Mathematics 2014年第12期57卷 2635-2648页

作者： ZHANG MuMing LIU Xu School of Mathematics and Statistics Northeast Normal University

This paper shows the existence of insensitizing controls for a class of nonlinear complex Ginzburg- Landau equations with homogeneous Dirichlet boundary conditions and arbitrarily located internal controller. When the nonlinearity in the equation satisfies a suitable superlinear growth condition at infinity, the existence of insensitizing controls for the corresponding semilinear Ginzburg-Landau equation is proved. Meanwhile, if the nonlinearity in the equation is only a smooth function without any additional growth condition, a local result on insensitizing controls is obtained. As usual, the problem of insensitizing controls is transforlned into a suitable controllability problem for a coupled system governed by a semilinear complex Ginzburg-Landau equation and a linear one through one control. The key is to establish an observability inequality for a coupled linear Ginzburg-Landau system with one observer.

关键词： insensitizing controls controllability Ginzburg-Landau equation

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Controllability of Quasilinear Parabolic Equations and Application

Controllability of Quasilinear Parabolic Equations and Appli...

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第二十九届中国控制会议

作者： LIU Xu School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,P.R.China

This paper addresses mainly the controllability of multi-dimensional quasilinear parabolic equations and some related control *** that the nonlinearity appearing in the principal operator brings new difficulty,which is different from the semilinear case ***,due to the time-irreversibility,previous approaches solving successfully the controllability of quasilinear hyperbolic equations do not work for this *** hereby need to develop a delicate Carleman estimate-based approach and solve the controllability problem in the frame of classical *** point is to establish the desired regularity on the control function for the linearized *** approach turns out to be quite general,and therefore,it can be applied to establish the local null controllability of both quasilinear parabolic equations and quasilinear Ginzburg-Landau ***,as its application,we also show the existence of insensitizing controls for quasilinear parabolic equations.

关键词： Local Null Controllability Quasilinear Parabolic Equation Ginzburg-Landau Equation insensitizing controls

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