共查询到20条相似文献,搜索用时 15 毫秒
1.
By means of a Carleman estimate, we obtain several observability inequalities by internal observation for hyperbolic equations with lower-order terms. Also, we apply our observability results to an exact controllability problem and an inverse wave source problem. 相似文献
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Nelia Charalambous 《Journal of Differential Equations》2007,233(1):291-312
In this paper we consider the Hodge Laplacian on differential k-forms over smooth open manifolds MN, not necessarily compact. We find sufficient conditions under which the existence of a family of logarithmic Sobolev inequalities for the Hodge Laplacian is equivalent to the ultracontractivity of its heat operator.We will also show how to obtain a logarithmic Sobolev inequality for the Hodge Laplacian when there exists one for the Laplacian on functions. In the particular case of Ricci curvature bounded below, we use the Gaussian type bound for the heat kernel of the Laplacian on functions in order to obtain a similar Gaussian type bound for the heat kernel of the Hodge Laplacian. This is done via logarithmic Sobolev inequalities and under the additional assumption that the volume of balls of radius one is uniformly bounded below. 相似文献
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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
4.
在此综述性文章中,我们将回顾关于节点状态的精确边界能控性的已有结果,并对此主题之进一步研究给出若干建议 相似文献
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This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. 相似文献
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Terminal constraint optimal control problems with unbounded control operators are considered. It is shown that the optimal solutions can be represented in a feedback form via a solution of an appropriate Riccati equation. In particular, it is proved that, for systems described by partial differential equations with infinite speed of propagation, boundary exact null controllability can be realized in feedback form.This work was partially supported by the National Science Foundation, Grant No. DMS-89-02811, and by the Air Force Office of Scientific Research, Grant No. AFOSR-89-0511 DEF. 相似文献
9.
Yury Grabovsky Davit Harutyunyan 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(1):267-282
We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that are diffeomorphic to a circular cylindrical shell with zero principal longitudinal curvature and positive circumferential curvature, including, for example, cylindrical and conical shells with arbitrary convex cross sections. We prove that the best constant in the first Korn inequality scales like thickness to the power 3/2 for a wide range of boundary conditions at the thin edges of the shell. Our methodology is to prove, for each of the three mutually orthogonal two-dimensional cross-sections of the shell, a “first-and-a-half Korn inequality”—a hybrid between the classical first and second Korn inequalities. These three two-dimensional inequalities assemble into a three-dimensional one, which, in turn, implies the asymptotically sharp first Korn inequality for the shell. This work is a part of mathematically rigorous analysis of extreme sensitivity of the buckling load of axially compressed cylindrical shells to shape imperfections. 相似文献
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高阶拟线性双曲型方程的精确边界能控性 总被引:1,自引:0,他引:1
YuLixin 《高校应用数学学报(英文版)》2005,20(2):127-141
By means of the existence and uniqueness of semi-global C^1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues ,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established. 相似文献
11.
In this paper, we deal with the approximate controllability for control systems described by a class of hemivariational inequalities. Firstly, we introduce the concept of mild solutions for hemivariational inequalities. Then the approximate controllability is formulated and proved by utilizing a fixed-point theorem of multivalued maps and properties of generalized Clarke subdifferential. 相似文献
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In this paper we examine computation of optimal control u* ofthe exact controllability problem (referred to as the constraintproblem) governed by the following type of linear parabolicdifferential equations: (y/t) + Ay = u in Q y = 0 on y(0) = y0 on where A is the second-order elliptic differential operator, is a bounded domain in k with smooth boundary , Q = (0, T)x , = (0, T) x and T > 0. This is achieved by approximatingu* through a sequence {un} of controls corresponding to unconstrainedproblems involving a penalty function arising from the controllabilityconstraint. 相似文献
13.
Ke WANG 《Frontiers of Mathematics in China》2011,6(3):545-555
Based on the theory of semi-global C
2 solution for 1-D quasilinear wave equations, the local exact boundary controllability of nodal profile for 1-D quasilinear
wave equations is obtained by a constructive method, and the corresponding global exact boundary controllability of nodal
profile is also obtained under certain additional hypotheses. 相似文献
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Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions. 相似文献
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We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can
be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index,
the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.
This work was supported by Key Academic Discipline of Zhejiang Province of China and National Natural Science Foundation of
China (Grant Nos. 10571014, 10631080, 10671019) 相似文献
18.
Zong Xiju~ Zhao Yi~ Yin Zhaoyang~ Chi Tao~ Dept.of Math. Zhongshan Univ. Guangzhou China. First Middle School of Tengzhou Shandong China. School of Control Science Engineering Jinan Univ. Jinan China 《高校应用数学学报(英文版)》2007,(3)
In this paper,the boundary control problem of a distributed parameter system described by the Schrdinger equation posed on finite intervalα≤x≤β: iyt yxx |y|~2y=0, y(α,t)=h_`1(t),y(β,t)=h_2(t)for t>0(S) is considered.It is shown that by choosing appropriate control inputs(h_j),(j=1,2)one can always guide the system(S)from a given initial stateφ∈H~s(α,β),(s∈R)to a terminal stateΨ∈H~s(α,β),in the time period[0,T].The exact boundary controllability is obtained by considering a related initial value control problem of Schrdinger equation posed on the whole line R.The discovered smoothing properties of Schrdinger equation have played important roles in our approach;this may be the first step to prove the results on boundary controllability of(semi-linear)nonlinear Schrdinger equation. 相似文献
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This paper deals with semilinear evolution equations with unbounded observation operators. Sufficient conditions are given
guaranteeing that the output function of a semilinear system is in L2loc([0, ∞); Y). We prove that the Lebesgue extension of the observation operators are invariant under nonlinear globally Lipschitz continuous
perturbations. Further, relations between the corresponding -extensions are studied. We show that exact observability of linear autonomous system is conserved under small Lipschitz perturbations.
The obtained results are illustrated by several examples.
相似文献
20.
Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square 总被引:1,自引:0,他引:1