共查询到20条相似文献,搜索用时 15 毫秒
1.
L. W. Wang 《Journal of Optimization Theory and Applications》2009,143(1):185-206
This paper considers the approximate controllability for a class of control systems governed by semilinear delay integrodifferential
equations with multiple delays. Sufficient conditions for approximate controllability are established by using the Schauder
fixed-point theorem. The results obtained improve some analogous existing results. Several examples are provided to illustrate
the application of the approximate controllability result. 相似文献
2.
The systems governed by delay differential equations come up in different fields of science and engineering but often demand the use of non-constant or state-dependent delays. The corresponding model equation is a delay differential equation with state-dependent delay as opposed to the standard models with constant delay. The concept of controllability plays an important role in physics and mathematics. In this paper, first we study the approximate controllability for a class of nonlinear fractional differential equations with state-dependent delays. Then, the result is extended to study the approximate controllability fractional systems with state-dependent delays and resolvent operators. A set of sufficient conditions are established to obtain the required result by employing semigroup theory, fixed point technique and fractional calculus. In particular, the approximate controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is approximately controllable. Also, an example is presented to illustrate the applicability of the obtained theory. 相似文献
3.
This paper is concerned with the zero Mach number limit of the
three-dimension- al compressible viscous magnetohydrodynamic
equations. More precisely, based on the local existence of the
three-dimensional compressible viscous magnetohydrodynamic
equations, first the convergence-stability principle is established.
Then it is shown that, when the Mach number is sufficiently small,
the periodic initial value problems of the equations have a unique
smooth solution in the time interval, where the incompressible
viscous magnetohydrodynamic equations have a smooth solution. When
the latter has a global smooth solution, the maximal existence time
for the former tends to infinity as the Mach number goes to zero.
Moreover, the authors prove the convergence of smooth solutions of
the equations towards those of the incompressible viscous
magnetohydrodynamic equations with a sharp convergence rate. 相似文献
4.
俞励超 《数学年刊A辑(中文版)》2019,40(4):417-426
研究了Poisson随机测度驱动的线性随机微分方程的近似能控性,通过对偶方法,得到了近似能控性的一个代数判据:由方程系数决定的某种不变空间V是退化空间{0}.此外,还给出了有限步计算验证该判据的程序算法. 相似文献
5.
D. Goreac 《Applied Mathematics and Optimization》2009,60(1):105-132
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system
with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the
dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded
operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability.
Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal
generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for
the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial
Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253–260, Chapman and
Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153–164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case. 相似文献
6.
Results providing sufficient conditions for the approximate controllability of a class of second-order abstract functional evolution equations governed by the generator of a strongly continuous cosine family of linear operators, together with nonlocal initial conditions, are developed. This work extends results included in recent work by Naito, Park, Zhou, and others. The abstract theory is then applied to a parabolic partial integrodifferential equation. 相似文献
7.
In this paper, the approximate controllability of neutral stochastic fractional differential equations involving nonlocal initial conditions is studied. By using Sadovskii’s fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of semilinear fractional stochastic differential equations with nonlocal conditions under the assumption that the corresponding linear system is approximately controllable. Finally, an application to a fractional partial stochastic differential equation with nonlocal initial condition is provided to illustrate the obtained theory. 相似文献
8.
Approximate Controllability of the System Governed by Double Coupled Semilinear Degenerate Parabolic Equations 下载免费PDF全文
This paper concerns the approximate controllability of the initial-boundary problem of double coupled semilinear degenerate parabolic equations. The equations are degenerate at the boundary, and the control function
acts in the interior of the spacial domain and acts only on one equation. We
overcome the difficulty of the degeneracy of the equations to show that the
problem is approximately controllable in $L^2$ by means of a fixed point theorem
and some compact estimates. That is to say, for any initial and desired data
in $L^2$, one can find a control function in $L^2$ such that the weak solution to the
problem approximately reaches the desired data in $L^2$ at the terminal time. 相似文献
9.
The basic concept of this research is to analyse the approximate controllability (AC) of a nonlinear delay integrodifferential evolution system (NDIDES) with random impulse of the type \begin{align*}&z''(\zeta)=\mathfrak{A}(\zeta)z(\zeta)+(\mathfrak{B}x)(\zeta)+\int_{0}^{\zeta}\mathcal{H}(\zeta, s,z(\beta(s))), \ \sigma_{q} <\zeta < \sigma_{q+1}, \ \zeta\in [\zeta_{0}, \mathcal{T}], \\ &z(\sigma_{q})=a_{q}(\tau_{q})z(\sigma^{-}_{q}), ~~q = 1,2,\ldots,\\ &z_{\zeta_{0}}=\upsilon,\end{align*} by assuming that the linear system is approximately controllable. The existence and uniqueness of the mild solution to above system have been determined by using the Banach contraction principle and trajectory accessible sets. We generalize the results for NDIDES with and without fixed-type impulsive moments. 相似文献
10.
W. Bian 《Acta Mathematica Hungarica》1998,81(1-2):41-57
The relations between the (strong) reachable sets of the semilinear evolution equation systems x′(t) + A(t)x(t) = f(t, x(t), u(t)) + Hu(t), x′(t) + A(t)x(t) = f(t, x(t), Hu(t)) + Hu(t) on a Banach space, and their corresponding linear systems are studied. Compared with previous results, the systems considered here are more general (f is not independent of the control u), no compactness assumptions on A or f are imposed in some of our main results, and we suppose f is a set-contraction rather than Lipschitz and have less restriction on the contraction coefficient. Other kinds of conditions are involved to guarantee the approximate controllability. 相似文献
11.
12.
Jong Uhn Kim 《Applied Mathematics and Optimization》2003,49(1):81-98
In this paper we discuss the controllability
of a wave equation with random noise.
Our main tools are the Ito representation theorem and
an adaptation of the Hilbert uniqueness method for the
exact controllability of deterministic equations. 相似文献
13.
In this paper we discuss the controllability
of a wave equation with random noise.
Our main tools are the Ito representation theorem and
an adaptation of the Hilbert uniqueness method for the
exact controllability of deterministic equations. 相似文献
14.
QuanSenJIU ChengHE 《数学学报(英文版)》2004,20(4):695-708
In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T]. Five sufficient conditions are given. Our results are motivated by two main ideas: one is to control the accumulation of vorticity alone; the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations. 相似文献
15.
Quan Sen JIU Department of Mathematics Capital Normal University Beijing P.R.China Cheng HE Institute of Applied Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing P.R.China 《应用数学学报(英文版)》2004,(4)
In this paper we are interested in the sufficient conditions which guarantee the regularityof solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T].Fivesufficient conditions are given.Our results are motivated by two main ideas:one is to control theaccumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of3-D Euler equations to 3-D ideal magnetohydrodynamic equations. 相似文献
16.
17.
Nadav Yesha 《Annales Henri Poincare》2013,14(7):1801-1836
In this paper, we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this operator are the eigenfunctions of the Laplacian which vanish at the scatterer, together with a set of new eigenfunctions (perturbed eigenfunctions). We first show that for a point scatterer on the standard torus all of the perturbed eigenfunctions are uniformly distributed in configuration space. Then we investigate the same problem for a point scatterer on a flat torus with some irrationality conditions, and show uniform distribution in configuration space for almost all of the perturbed eigenfunctions. 相似文献
18.
X. Zhang 《Applied Mathematics and Optimization》2000,41(2):155-170
In this paper we obtain two exact internal controllability results of Maxwell's equations in a general region by using multiplier
techniques. The first one is exact controllability in a short time, in which we obtain the ``optimal" (observability) estimates
when the location and the shape of the controller is fixed. What happens if we allow the controller to change? Under some
conditions, we show that by doing that the system can be exactly controllable within any given time duration, which is our
second exact controllability result.
Accepted 30 September 1998 相似文献
19.
In this paper, the approximate controllability for a class of semilinear delay control systems of fractional order is proved
under the natural assumption that the linear system is approximately controllable. The existence and uniqueness of the mild
solution is also proved under suitable assumptions. An example is given to illustrate our main results. 相似文献