共查询到20条相似文献,搜索用时 15 毫秒
1.
Bernhard H. Haak Peer Christian Kunstmann 《Integral Equations and Operator Theory》2006,55(4):497-533
We study linear systems, described by operators A, B, C for which the state space X is a Banach space.We suppose that − A generates a bounded analytic semigroup and give conditions for admissibility of B and C corresponding to those in G. Weiss’ conjecture. The crucial assumptions on A are boundedness of an H∞-calculus or suitable square function estimates, allowing to use techniques recently developed by N. Kalton and L. Weis. For observation spaces Y or control spaces U that are not Hilbert spaces we are led to a notion of admissibility extending previous considerations by C. Le Merdy. We also obtain a characterisation of wellposedness for the full system. We give several examples for admissible operators
including point observation and point control. At the end we study a heat equation in X = Lp(Ω), 1 < p < ∞, with boundary observation and control and prove its wellposedness for several function spaces Y and U on the boundary ∂Ω. 相似文献
2.
Christopher T.H. Baker Gennady Bocharov Eugene Parmuzin Fathalla Rihan 《Journal of Computational and Applied Mathematics》2009
The problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay-differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) rôles for well-defined adjoints and ‘quasi-adjoints’, and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints. 相似文献
3.
In this paper the problem of exponential stability of the zero state equilibrium of a discrete-time time-varying linear equation
described by a sequence of linear positive operators acting on an ordered finite dimensional Hilbert space is investigated.
The class of linear equations considered in this paper contains as particular cases linear equations described by Lyapunov
operators or symmetric Stein operators as well as nonsymmetric Stein operators. Such equations occur in connection with the
problem of mean square exponential stability for a class of difference stochastic equations affected by independent random
perturbations and Markovian jumping as well us in connection with some iterative procedures which allow us to compute global
solutions of discrete time generalized symmetric or nonsymmetric Riccati equations.
The exponential stability is characterized in terms of the existence of some globally defined and bounded solutions of some
suitable backward affine equations (inequalities) or forward affine equations (inequalities). 相似文献
4.
This paper deals with the stability of linear time-varying systems involving switches through time between different parameterizations of a dynamic linear time-varying system. Graph theory is used to describe the combinations of possible switches of the various sets of parameterizations which ensure the stability of the configurations. Each graph vertex is associated with a particular parameterization while edges (arcs) are associated with switches between the graphs (directed graphs or digraphs). An axiomatic framework is first established concerned with previously known stability results from systems theory related to the achievement of stability when switches between several parameterizations of a dynamic system take place. The axiomatic context is then used to obtain stability results mainly based on the topology of the links between the various configurations associated with a state-trajectory as well as on the nature of the vertices related to the stability of the various isolated parameterizations. 相似文献
5.
T. Gayer 《Journal of Differential Equations》2004,201(1):177-200
Control sets, i.e., maximal sets of approximate controllability, are described for systems with parameter-dependent control range. If the so-called inner-pair condition is satisfied, it is known that generically they change continuously under parameter variation while mergers of control sets produce discontinuous transitions. The inner-pair condition is proved for a class of control-affine systems on . Furthermore, continuity results for exit and entrance boundaries of control sets are given both for one control set that changes continuously and for two merging control sets. The results are illustrated by means of the controlled escape equation. 相似文献
6.
7.
The solvability of integral equations of the form
and the behaviour of the solution x at infinity are investigated. Conditions on k and on a weight function w are obtained which ensure that the integral operator K with kernel k is bounded as an operator on Xw, where Xw denotes the weighted space of those continuous functions defined on the half-line which are O(w(s)) as
We also derive conditions on w and k which imply that the spectrum and essential spectrum of K on Xw are the same as on BC[0,). In particular, the results apply when
when the integral equation is of Wiener-Hopf type. In this case we show that our results are particularly sharp. 相似文献
8.
Thomas Stoll 《Journal of Number Theory》2008,128(5):1157-1181
We characterize decomposition over C of polynomials defined by the generalized Dickson-type recursive relation (n?1)
9.
Marianne Chapouly 《Journal of Differential Equations》2009,247(7):2094-607
In this paper, we deal with a two-dimensional Navier-Stokes system in a rectangle with Navier slip boundary conditions on the horizontal sides. We establish the global null controllability of the system by controlling the normal component and the vorticity of the velocity on the vertical sides. The linearized control system around zero is controllable but one does not know how to deduce global controllability results for the nonlinear system. Our proof uses the return method together with a local exact controllability result by Fursikov and Imanuvilov. 相似文献
10.
Valeri Obukhovskii Pietro Zecca 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(8):2765-2777
We introduce the notion of a multivalued causal operator and consider an abstract Cauchy problem in a Banach space for various classes of functional inclusions with causal operators. The methods of the topological degree theory for condensing maps are applied to obtain local and global existence results for this problem and to study the continuous dependence of a solution set on initial data. As application we generalize some existence results for semilinear functional differential inclusions and Volterra integro-differential inclusions with delay. 相似文献
11.
12.
We prove general theorems on mean ergodicity and mean stability
of regularized solution families with respect to fairly general summability
methods. They can be applied to integrated solution families, integrated semigroups
and cosine functions. In particular, through applications with modified
Cesàro, Abel, Gauss, and Gamma like summability methods we deduce particular
results on mean ergodicity and mean stability of polynomially bounded
C0-semigroups and cosine operator functions. 相似文献
13.
Alexander Kheifets 《Integral Equations and Operator Theory》1995,21(3):334-341
This paper gives a negative answer to a question due to V.M. Adamjan, D.Z. Arov and M.G. Krein, and (what is the same) gives a counterexample to D.Sarason's conjecture* concerning exposed points inH
1. 相似文献
14.
15.
Robert Carroll 《Acta Appl Math》1986,6(2):109-184
This article represents a survey of transmutation ideas and their interaction with typical physical problems. For linear second-order differential operatorsP andQ one deals with canonical connectionsB:PQ (transmutations) satisfyingQB=BP and the related transport of structure between the theories ofP andQ. One can study in an intrinsic manner, e.g., Parseval formulas, eigenfunction expansions, integral transform, special functions, inverse problems, integral equations, and related stochastic filtering and estimation problems, etc. There are applications in virtually any area where such operators arise. 相似文献
16.
On the resolvent condition in the Kreiss Matrix Theorem 总被引:3,自引:0,他引:3
The Kreiss Matrix Theorem asserts the uniform equivalence over allN ×N matrices of power boundedness and a certain resolvent estimate. We show that the ratio of the constants in these two conditions grows linearly withN, and we obtain the optimal proportionality factor up to a factor of 2. Analogous results are also given for the related problem involving matrix exponentialse
At
. The proofs make use of a lemma that may be of independent interest, which bounds the arc length of the image of a circle in the complex plane under a rational function.Dedicated to Germund Dahlquist on the occasion of his sixtieth birthday.Research supported by NSF Mathematical Sciences Postdoctoral Fellowships, by the Courant Institute of Mathematical Sciences, and by the National Aeronautics and Space Administration under Contract No. NAS1-17070 while the authors were in residence at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665. 相似文献
17.
M. N. Spijker 《BIT Numerical Mathematics》1991,31(3):551-555
In the Kreiss matrix theorem the power boundedness ofN ×N matrices is related to a resolvent condition on these matrices. LeVeque and Trefethen proved that the ratio of the constants in these two conditions can be bounded by 2eN. They conjectured that this bound can be improved toeN.In this note the conjecture is proved to be true. The proof relies on a lemma which provides an upper bound for the arc length of the image of the unit circle in the complex plane under a rational function. This lemma may be of independent interest. 相似文献
18.
The sets of solutions to the Lorenz equations that exist backward in time and are bounded at an exponential rate determined by the eigenvalues of the linear part of the equation are examined. The set associated with the middle eigenvalue is shown to project surjectively onto a plane, thereby providing a lower estimate for its dimension. Specific bounds are also found for a cone containing this set. 相似文献
19.
Pham Viet Hai 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):4390-4396
In this paper, we will consider the concept “linear skew-evolution semiflows” and extend theorems of R. Datko, S. Rolewicz, Zabczyk and J.M.A.M van Neerven for this case [15]. 相似文献
20.
This paper presents necessary and sufficient conditions for uniform exponential trichotomy of nonlinear evolution operators
in Banach spaces. Thus are obtained results which extend well-known results for uniform exponential stability in the linear
case.
相似文献