共查询到20条相似文献,搜索用时 31 毫秒
1.
ZHANG Xu 《数学年刊B辑(英文版)》1999,20(3):378-384
1.IntroductionConsiderthefollowingsemilinearwaveequationwithalocallydistributedcofltroller:whereI~g,11~$,nCR"isaboundeddomainwithaboundaryoffECI)andforeachtE[0,co),G(t)isasubdomainoffi.Intheabove,y(t,x)isthestateandXG(t)(x)u(t,x)isthecolltrol.Thus,u(t,x)istheintensityofthecontrolactionandG(t)isthelocationandtheshapeofthecontroller.Wewillallowthelocationandtheshapeofthecontrollertochange.LetU=Lfo.(0'co;L'(fl))andletQbeafamilyofset--valuedfunctionsG(t)definedon[0,co)takingsubdomainsoffias… 相似文献
2.
关于耗散波动方程精确能控性的奇异极限的一个注记 总被引:1,自引:1,他引:0
本文在比文献[1]更一般的几何控制条件下,分析了具齐次Dirichlet边界条件的耗散波动方程精确能控性的奇异摄动问题.结论是由这类波动方程的精确能控性可得到热传导方程的精确零能控性. 相似文献
3.
S. Guerrero O.Yu. Imanuvilov 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2007,24(6):897-906
In this paper we deal with the viscous Burgers equation. We study the exact controllability properties of this equation with general initial condition when the boundary control is acting at both endpoints of the interval. In a first result, we prove that the global exact null controllability does not hold for small time. In a second one, we prove that the exact controllability result does not hold even for large time. 相似文献
4.
Chunxiong Zheng 《计算数学(英文版)》2007,25(6):730-745
In this paper we consider the numerical solution of the one-dimensional heat equation on unbounded domains. First an exact semi-discrete artificial boundary condition is derived by discretizing the time variable with the Crank-Nicolson method. The semi-discretized heat equation equipped with this boundary condition is then proved to be unconditionally stable, and its solution is shown to have second-order accuracy. In order to reduce the computational cost, we develop a new fast evaluation method for the convolution operation involved in the exact semi-discrete artificial boundary condition. A great advantage of this method is that the unconditional stability held by the semi-discretized heat equation is preserved. An error estimate is also given to show the dependence of numerical errors on the time step and the approximation accuracy of the convolution kernel. Finally, a simple numerical example is presented to validate the theoretical results. 相似文献
5.
In this paper, we deal with controllability properties of linear and nonlinear Korteweg-de Vries equations in a bounded interval. The main part of this paper is a result of uniform controllability of a linear KdV equation in the limit of zero-dispersion. Moreover, we establish a result of null controllability for the linear equation via the left Dirichlet boundary condition, and of exact controllability via both Dirichlet boundary conditions. As a consequence, we obtain some local exact controllability results for the nonlinear KdV equation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
This paper is concerned with the exact controllability of nonlinear third order dispersion equation with infinite distributed delay. Sufficient conditions are formulated and proved for the exact controllability of this system. Without imposing a compactness condition on the semigroup, we establish controllability results by using a fixed point analysis approach. 相似文献
7.
Chun-xiong Zheng Hou-de Han 《计算数学(英文版)》2002,20(6):591-598
A finite element method for the solution of Oseen equation in exterior domain is proposed. In this method, a circular artificial boundary is introduced to make the computational domain finite. Then, the exact relation between the normal stress and the prescribed velocity field on the artificial boundary can be obtained analytically. This relation can serve as an boundary condition for the boundary value problem defined on the finite domain bounded by the artificial boundary. Numerical experiment is presented to demonstrate the performance of the method. 相似文献
8.
In this paper, we study one-dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation by Hilbert uniqueness method when the control acts on the nondegenerate boundary. Moreover, an explicit expression for the controllability time is given. 相似文献
9.
The authors prove the global exact boundary controllability for the cubic semi-linear wave equation in three space dimensions, subject to Dirichlet, Neumann, or any other kind of boundary controls which result in the well-posedness of the corresponding initial-boundary value problem. The exponential decay of energy is first established for the cubic semi-linear wave equation with some boundary condition by the multiplier method, which reduces the global exact boundary controllability problem to a local one. The proof is carried out in line with [2, 15]. Then a constructive method that has been developed in [13] is used to study the local problem. Especially when the region is star-complemented, it is obtained that the control function only need to be applied on a relatively open subset of the boundary. For the cubic Klein-Gordon equation, similar results of the global exact boundary controllability are proved by such an idea. 相似文献
10.
Zhiqiang Wang 《Mathematical Methods in the Applied Sciences》2007,30(11):1311-1327
In this paper, we first show that quite different from the autonomous case, the exact boundary controllability for non‐autonomous wave equations possesses various possibilities. Then we adopt a constructive method to establish the exact boundary controllability for one‐dimensional non‐autonomous quasilinear wave equations with various types of boundary conditions. Finally, we apply the results to multi‐dimensional quasilinear wave equation with rotation invariance. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
11.
We study the boundary exact controllability for the semilinear Schrödinger equation defined on an open, bounded, connected set Ω of a complete, n-dimensional, Riemannian manifold M with metric g. We prove the locally exact controllability around the equilibria under some checkable geometrical conditions. Our results show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and equilibria of the semilinear Schrödinger equation. We then establish the globally exact controllability in such a way that the state of the semilinear Schrödinger equation moves from an equilibrium in one location to an equilibrium in another location. 相似文献
12.
Abstract
In this note we analyze the exact controllability of singularly perturbed damped wave equations under more general geometric
control condition than that of [1]. We show that the null controllability of the heat equation can be obtained as a singular
limit of the exact controllability of such sorts of wave equations.
The work of Yuping Tang was carried out when she visited the “School of Mathematics, Sichuan University”.
The work of Xu Zhang was partially supported by NSF of China under Grant 19901024 相似文献
13.
Local exact controllability of Schr\"{o}dinger equation with Sturm- Liouville boundary value problems 下载免费PDF全文
In this paper, we investigate the controllability of 1D bilinear Schr\"{o}dinger equation with Sturm-Liouville boundary value condition. The system represents a quantumn particle controlled by an electric field. K. Beauchard and C. Laurent have proved local controllability of 1D bilinear Schr\"{o}dinger equation with Dirichlet boundary value condition in some suitable Sobolev space based on the classical inverse mapping theorem. Using a similar method, we extend this result to Sturm-Liouville boundary value proplems. 相似文献
14.
Luciano Pandolfi 《Applied Mathematics and Optimization》2005,52(2):143-165
In this paper we give a semigroup-based definition of the solution of the Gurtin-Pipkin equation with Dirichlet boundary conditions.
It turns out that the dominant term
of the input-to-state map is the control to displacement operator of the wave equation. This operator is surjective if the
time interval is long enough. We use this observation in order to prove exact controllability in finite time of the Gurtin-Pipkin
equation. 相似文献
15.
This paper deals with boundary exact controllability for the dynamics governed by the wave equation with variable coefficients in time and space, subject to Dirichlet or Neumann boundary controls. The observability inequalities are established by the Riemannian geometry method under some geometric conditions. 相似文献
16.
Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions 下载免费PDF全文
Yue Wang Günter Leugering Tatsien Li 《Mathematical Methods in the Applied Sciences》2017,40(10):3808-3820
By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
Boundary Controllability for the Quasilinear Wave Equation 总被引:1,自引:0,他引:1
Peng-Fei Yao 《Applied Mathematics and Optimization》2010,61(2):191-233
We study the boundary exact controllability for the quasilinear wave equation in high dimensions. Our main tool is the geometric
analysis. We derive the existence of long time solutions near an equilibrium, prove the locally exact controllability around
the equilibrium under some checkable geometrical conditions. We then establish the globally exact controllability in such
a way that the state of the quasilinear wave equation moves from an equilibrium in one location to an equilibrium in another
location under some geometrical conditions. The Dirichlet action and the Neumann action are studied, respectively. Our results
show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and equilibria
of the quasilinear wave equation. A criterion of exact controllability is given, which based on the sectional curvature of
the Riemann metric. Some examples are presented to verify the global exact controllability. 相似文献
18.
The exact controllability and observability for a heat equation with hyperbolic memory kernel in anisotropic and nonhomogeneous media are considered. Due to the appearance of such a kind of memory, the speed of propagation for solutions to the heat equation is finite and the corresponding controllability property has a certain nature similar to hyperbolic equations, and is significantly different from that of the usual parabolic equations. By means of Carleman estimate, we establish a positive controllability and observability result under some geometric condition. On the other hand, by a careful construction of highly concentrated approximate solutions to hyperbolic equations with memory, we present a negative controllability and observability result when the geometric condition is not satisfied. 相似文献
19.
Ke Wang 《Mathematical Methods in the Applied Sciences》2011,34(3):315-324
Based on the local exact boundary controllability for 1‐D quasilinear wave equations, the global exact boundary controllability for 1‐D quasilinear wave equations in a neighborbood of any connected set of constant equilibria is obtained by an extension method. Similar results are also given for a kind of general 1‐D quasilinear hyperbolic equations. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
20.
R.K. George A.K. Nandakumaran 《Journal of Mathematical Analysis and Applications》2007,332(2):1028-1044
Exact controllability of a nonlinear dispersion system has been studied. This work extends the work of Russell and Zhang [D.L. Russell, B.Y. Zhang, Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain, SIAM J. Control Optim. 31 (1993) 659-676], in which the authors considered a linear dispersion system. We obtain controllability results using two standard types of nonlinearities, namely, Lipschitzian and monotone. We also obtain the exact controllability of the same system through the approach of Integral Contractors which is a weaker condition than Lipschitz condition. 相似文献