共查询到20条相似文献,搜索用时 0 毫秒
1.
Sergei A. Avdonin Boris P. Belinskiy Sergei A. Ivanov 《Applied Mathematics and Optimization》2009,60(1):71-103
We study the exact controllability problem for a ring under stretching tension that varies in time. We are looking for a couple
of forces, which drive the state solution to rest. We show that applying two forces is necessary for controllability and the
ring is controllable in the time interval greater than the optical length of the string. We also explain why one force would
not be enough to control the ring. We use the method of moments to reduce the controllability problem to a moment problem
for the controlling forces. The solution of that problem is based on an auxiliary basis property result. Both method of moments
and proof of the basis property are developed for the model with time-dependent parameters.
S.A.’s research was supported in part by the NSF, grant ARC–0724860.
B.B.’s research was supported in part by University of Tennessee at Chattanooga Faculty Research Grant.
S.I.’s research was supported in part by the Russian Foundation for Basic Research, grants 08-01-00595a and 08-01-00676a. 相似文献
2.
Evgeniy Pustylnik 《Journal of Mathematical Analysis and Applications》2008,344(2):788-798
We give necessary and sufficient conditions for the set of measurable functions to be a normable linear space. We also give a complete characterization of all spaces B that can be represented in the form B=Y(A) for some space A and of all spaces A that can appear in such representations. 相似文献
3.
We consider the system consisting of K coupled acoustic channels with the different sound velocities . Channels are interacting at any point via the pressure and its time derivatives. Using the moment approach and the theory of exponential families with vector coefficients we establish two controllability results: the system is exactly controllable if(i) the control in the jth channel acts longer than the double travel time of a wave from the start to the end of the j-th channel;(ii) all controls act more than or equal to the maximal double travel time. 相似文献
4.
Stochastic second-order partial differential equations of evolution type are considered in one space dimension. Existence and uniqueness results are given in weighted Sobolev spaces of functions given on an interval in the space variable. 相似文献
5.
6.
《Journal of Functional Analysis》2023,284(1):109739
We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces to be bounded. The condition has a form of a simple integral inequality involving Young and weight functions. We provide an example with Matuszewska-Orlicz indices of involved Orlicz norm equal to one. The main tool is the molecular decomposition of functions from a BV space. 相似文献
7.
Let μ be a finite positive Borel measure supported in [−1,1] and introduce the discrete Sobolev-type inner productwhere the mass points ak belong to [−1,1], Mk,i0, i=0,…,Nk−1, and Mk,Nk>0. In this paper, we study the asymptotics of the Sobolev orthogonal polynomials by comparison with the orthogonal polynomials with respect to the measure μ and we prove that they have the same asymptotic behaviour. We also study the pointwise convergence of the Fourier series associated to this inner product provided that μ is the Jacobi measure. We generalize the work done by F. Marcellán and W. Van Assche where they studied the asymptotics for only one mass point in [−1,1]. The same problem with a finite number of mass points off [−1,1] was solved by G. López, F. Marcellán and W. Van Assche in a more general setting: they consider the constants Mk,i to be complex numbers. As regards the Fourier series, we continue the results achieved by F. Marcellán, B. Osilenker and I.A. Rocha for the Jacobi measure and mass points in
. 相似文献
8.
Mathematical Notes - 相似文献
9.
The authors study vanishing viscosity limits of solutions to the 3-dimensional
incompressible Navier-Stokes system in general smooth domains with curved boundaries
for a class of slip boundary conditions. In contrast to the case of flat boundaries, where the
uniform convergence in super-norm can be obtained, the asymptotic behavior of viscous
solutions for small viscosity depends on the curvature of the boundary in general. It
is shown, in particular, that the viscous solution converges to that of the ideal Euler
equations in C([0, T];H1(Ω)) provided that the initial vorticity vanishes on the boundary
of the domain. 相似文献
10.
Salim A. Messaoudi Ala A. Talahmeh 《Mathematical Methods in the Applied Sciences》2017,40(18):6976-6986
We consider, in this paper, the following nonlinear equation with variable exponents: where a,b>0 are constants and the exponents of nonlinearity m,p, and r are given functions. We prove a finite‐time blow‐up result for the solutions with negative initial energy and for certain solutions with positive energy. 相似文献
11.
12.
We prove that the Sobolev embedding operator S
d,k,p :
, where 1/s=1/p-k/d , is (v,1) -absolutely summing for appropriate v > 1 . The result is optimal for s
2 . 相似文献
13.
Shang Quan Bu 《数学学报(英文版)》2010,26(7):1223-1232
We study the well-posedness of the equations with fractional derivative D^αu(t) = Au(t) + f(t),0≤ t ≤ 2π, where A is a closed operator in a Banach space X, α 〉 0 and D^α is the fractional derivative in the sense of Weyl. Using known results on LP-multipliers, we give necessary and/or sufficient conditions for the LP-well-posedness of this problem. The conditions we give involve the resolvent of A and the Rademacher boundedness. Corresponding results on the well-posedness of this problem in periodic Besov spaces, periodic Triebel-Lizorkin spaces and periodic Hardy spaces are also obtained. 相似文献
14.
Christine Thomas-Agnan 《Numerical Algorithms》1996,13(1):21-32
For an open subset of , an integer,m, and a positive real parameter , the Sobolev spacesH
m
() equipped with the norms: u2=u(t)2dt+(1/2m
u
(m)(t)2 constitute a family of reproducing kernel Hilbert spaces. When is an open interval of the real line, we describe the computation of their reproducing kernels. We derive explicit formulas for these kernels for all values ofm in the case of the whole real line, and form=1 andm=2 in the case of a bounded open interval.This research was partly supported by NSF Grant DMS-9002566. 相似文献
15.
In this paper, the pole assignment problem is considered for a class of distributed parameter systems with unbounded input
element and with multiple spectral structure. A formula on the spectrum of the closed loop operator is proved and a formula
of pole assignment is obtained. Finally, an example concerning a beam vibration is given.
This work is supported by the National Natural Sciences Foundation of China and the National Key Project of China, and partly
by the Post Doctoral Science Foundation of China and the Youth Science Foundation of Shanxi. 相似文献
16.
In this paper, we obtain both global and local controllability results for a general nonautonomous predator-prey system using some techniques of nonlinear functional analysis such as the Schauder fixed-point theorem and contraction mapping principle.The first author would like to thank the Department of Science and Technology of India for sponsoring part of this work through Grant No. DST 12(21)/84-STP II. 相似文献
17.
M. A. Christodoulou P. N. Paraskevopoulos 《Journal of Optimization Theory and Applications》1985,45(1):53-72
The problems of solvability, controllability, and observability for the singular systemKx(t)=Ax(t)+Bu(t) are studied, whereK is a singular, square matrix andu(t) is a complex vector function sufficiently differentiable. The classical theories of matrix pencils are first related to the solvability of singular systems. Then, the concepts of reachability, controllability, and observability of regular systems are extended to singular systems. Finally, the set of reachable states is described. The proposed matrix conditions for testing the controllability and observability of singular systems are simple and always feasible. 相似文献
18.
We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u 0 ∈ H 3/4+ (?) whose restriction belongs to H l ((b, ∞)) for some l ∈ ?+ and b ∈ ? we prove that the restriction of the corresponding solution u(·, t) belongs to H l ((β, ∞)) for any β ∈ ? and any t ∈ (0, T). Thus, this type of regularity propagates with infinite speed to its left as time evolves. 相似文献
19.
A. Margheri 《Journal of Optimization Theory and Applications》1990,66(1):61-69
The problem of the 0-local controllability of a linear control system when the origin does not belong to the constraint set is considered. Sufficient conditions for the 0-local controllability are presented here, extending a previous theorem by Saperstone and connecting this property with the distance of the constraint set from the origin. 相似文献