共查询到20条相似文献,搜索用时 15 毫秒
1.
V. N. Denisov 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):91-103
We obtain sharp sufficient conditions on the growth of lower order coefficients of a second-order parabolic equation under
which a solution to the Cauchy problem stabilizes to zero uniformly in x on every compact set K ∈ ℝ
N
in some classes of growing initial functions. 相似文献
2.
I. V. Gaishun 《Differential Equations》2009,45(10):1497-1506
We obtain conditions for the existence of a linear feedback providing the existence of a family (N
t
) of subspaces such that this family is invariant under the closed system and the output variable is zero on all motions lying
in this family. 相似文献
3.
V. N. Denisov 《Journal of Mathematical Sciences》2004,120(3):1313-1327
The paper deals with the study of sufficient conditions on the coefficients of a second-order partial differential equation, ensuring the stabilization to zero of the solution of the Cauchy problem uniformly in x on any compact set K
N
for any continuous initial function u
0(x), growing at infinity not faster than some power of |x|
m
, m > 0. 相似文献
4.
N. U. Ahmed 《Mathematical and Computer Modelling》1988,10(12):891-900
We consider the problem of rigorous modeling and stabilization of large satellites with several flexible appendages, such as a boom, tower, solar panel etc., all located arbitrarily on the rigid bus. The complete dynamics of the system is described by a set of hyperbolic partial differential equations coupled with a set of ordinary differential equations. These two sets of equations are very strongly coupled and describe the interaction among the rigid and the flexible members of the spacecraft. We propose feedback control schemes that make the system asymptotically stable in the sense that all the bus angular motions and the vibrations of the elastic members eventually decay to zero. We also present simulation results illustrating stabilization of the spacecraft by the feedback controls. 相似文献
5.
We will consider the relation between the number of positive standing waves solutions for a class of coupled nonlinear Schrödinger system in RN and the topology of the set of minimum points of potential V(x). The main characteristics of the system are that its functional is strongly indefinite at zero and there is a lack of compactness in RN. Combining the dual variational method with the Nehari technique and using the Concentration-Compactness Lemma, we obtain the existence of multiple solutions associated to the set of global minimum points of the potential V(x) for ? sufficiently small. In addition, our result gives a partial answer to a problem raised by Sirakov about existence of solutions of the perturbed system. 相似文献
6.
Iryna Ryzhkova 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):246-261
We discuss the problem of non-linear oscillations of a clamped thermoelastic plate in a subsonic gas flow. The dynamics of
the plate is described by von Kármán system in the presence of thermal effects. No mechanical damping is assumed. To describe
the influence of the gas flow we apply the linearized theory of potential flows. Our main result states that each weak solution
of the problem considered tends to the set of the stationary points of the problem.
A similar problem was considered in [27], but with rotational inertia accounted for, i.e. with the additional term −αΔutt,α > 0, and the same result on stabilization was obtained. There was introduced the decomposition of the solution such that
the one term tends to zero and the other is compact in special (“local energy”) topology. This decomposition enables us to
prove the main result. But the case of rotational inertia neglected (α = 0) appears more difficult. Low a priori smoothness
of ut in the case α = 0 prevents us to construct such a decomposition. In order to prove additional smoothness of ut we use analyticity of the corresponding thermoelastic semigroup proved in [25].
The isothermal variant of this problem with additional mechanical damping term −εΔut
, ε > 0 was considered in [13] and stabilization to the set of stationary solutions to the problem was proved. The problem,
considered in the present work can also be regarded as an extension of the result of [18] to the case when gas occupies an
unbounded domain. 相似文献
7.
We study the local stabilization of the three-dimensional Navier–Stokes equations around an unstable stationary solution w, by means of a feedback boundary control. We first determine a feedback law for the linearized system around w. Next, we show that this feedback provides a local stabilization of the Navier–Stokes equations. To deal with the nonlinear term, the solutions to the closed loop system must be in H3/2+ε,3/4+ε/2(Q), with 0<ε. In [V. Barbu, I. Lasiecka, R. Triggiani, Boundary stabilization of Navier–Stokes equations, Mem. Amer. Math. Soc. 852 (2006); V. Barbu, I. Lasiecka, R. Triggiani, Abstract settings for tangential boundary stabilization of Navier–Stokes equations by high- and low-gain feedback controllers, Nonlinear Anal. 64 (2006) 2704–2746], such a regularity is achieved with a feedback obtained by minimizing a functional involving a norm of the state variable strong enough. In that case, the feedback controller cannot be determined by a well posed Riccati equation. Here, we choose a functional involving a very weak norm of the state variable. The compatibility condition between the initial state and the feedback controller at t=0, is achieved by choosing a time varying control operator in a neighbourhood of t=0. 相似文献
8.
V. A. Zaitsev 《Differential Equations》2015,51(12):1637-1648
We obtain new sufficient conditions for the local and global asymptotic stabilization of the zero solution of a nonlinear affine control system with discrete time and with constant coefficients by a continuous state feedback. We assume that the zero solution of the free system is Lyapunov stable. For systems with linear drift, we construct a bounded control in the problem of global asymptotic state and output stabilization. Corollaries for bilinear systems are obtained. 相似文献
9.
J. I. Abdullaev 《Theoretical and Mathematical Physics》2006,147(1):486-495
We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of
bound states N(k) is a nondecreasing function of the total quasimomentum of the system k ∈ [0, π]. We describe the set of discontinuity points of N(k) and evaluate the jump N(k +0) − N(k) at the discontinuity points. We establish that the bound-state energy z
n
(k) increases as the total quasimomentum k ∈ [0, π] increases.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 47–57, April, 2006. 相似文献
10.
Carlo Marchioro Piero Negrini 《NoDEA : Nonlinear Differential Equations and Applications》1999,6(4):473-499
We introduce a dynamical system strictly related to fluid mechanics and similar to the classical N point vortex system. In the first part we analyze the qualitative behavior of the time evolution and in particular we show
the properties of collapse and chaoticity. In the second part of the paper we investigate the relation of the dynamical system
with a system of N concentrated large enough smoke rings in an incompressible and inviscid fluid, with axial symmetry and without swirl. We
prove the rigorous connection between the two models at time zero for any N. The extension of the same result to any time is obtained only for a smoke ring alone, while for the general case it is just
a matter of conjecture.
Received June 1998; Revised November 1998 相似文献
11.
We consider symmetric flows of a viscous compressible barotropic fluid with a free boundary, under a general mass force depending both on the Eulerian and Lagrangian co‐ordinates, with arbitrarily large initial data. For a general non‐monotone state function p, we prove uniform‐in‐time energy bound and the uniform bounds for the density ρ, together with the stabilization as t → ∞ of the kinetic and potential energies. We also obtain H1‐stabilization of the velocity v to zero provided that the second viscosity is zero. For either increasing or non‐decreasing p, we study the Lλ‐stabilization of ρ and the stabilization of the free boundary together with the corresponding ω‐limit set in the general case of non‐unique stationary solution possibly with zones of vacuum. In the case of increasing p and stationary densities ρS separated from zero, we establish the uniform‐in‐time H1‐bounds and the uniform stabilization for ρ and v. All these results are stated and mainly proved in the Eulerian co‐ordinates. They are supplemented with the corresponding stabilization results in the Lagrangian co‐ordinates in the case of ρS separated from zero. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
In this paper, the boundary output feedback stabilization problem is addressed for a class of coupled nonlinear parabolic systems. An output feedback controller is presented by introducing a Luenberger‐type observer based on the measured outputs. To determine observer gains, a backstepping transform is introduced by choosing a suitable target system with nonlinearity. Furthermore, based on the state observer, a backstepping boundary control scheme is presented. With rigorous analysis, it is proved that the states of nonlinear closed‐loop system including state estimation and estimation error of plant system are locally exponentially stable in the L2norm. Finally, a numerical example is proposed to illustrate the effectiveness of the presented scheme. 相似文献
13.
Jan Florek 《Journal of Graph Theory》2014,75(4):355-357
Isaak posed the following problem. Suppose T is a tournament having a minimum feedback arc set, which induces an acyclic digraph with a hamiltonian path. Is it true that the maximum number of arc‐disjoint cycles in T equals the cardinality of minimum feedback arc set of T? We prove that the answer to the problem is in the negative. 相似文献
14.
The central model of this paper is anM/M/1 queue with a general probabilistic feedback mechanism. When a customer completes his ith service, he departs from the system with probability 1–p(i) and he cycles back with probabilityp(i). The mean service time of each customer is the same for each cycle. We determine the joint distribution of the successive sojourn times of a tagged customer at his loops through the system. Subsequently we let the mean service time at each loop shrink to zero and the feedback probabilities approach one in such a way that the mean total required service time remains constant. The behaviour of the feedback queue then approaches that of anM/G/1 processor sharing queue, different choices of the feedback probabilities leading to different service time distributions in the processor sharing model. This is exploited to analyse the sojourn time distribution in theM/G/1 queue with processor sharing.Some variants are also considered, viz., anM/M/1 feedback queue with additional customers who are always present, and anM/G/1 processor sharing queue with feedback. 相似文献
15.
We examine existence and stability of relative equilibria of the n-vortex problem specialized to the case where N vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero, the
weak vortices tend to a circle centered on the strong vortex. A special potential function of this limiting problem can be
used to characterize orbits and stability. Whenever a critical point of this function is nondegenerate, we prove that the
orbit can be continued via the Implicit Function Theorem, and its linear stability is determined by the eigenvalues of the
Hessian matrix of the potential. For N≥3 there are at least three distinct families of critical points associated to the limiting problem. Assuming nondegeneracy,
one of these families continues to a linearly stable class of relative equilibria with small and large circulation of the
same sign. This class becomes unstable as the small circulation passes through zero and changes sign. Another family of critical
points which is always nondegenerate continues to a configuration with small vortices arranged in an N-gon about the strong central vortex. This class of relative equilibria is linearly unstable regardless of the sign of the
small circulation when N≥4. Numerical results suggest that the third family of critical points of the limiting problem also continues to a linearly
unstable class of solutions of the full problem independent of the sign of the small circulation. Thus there is evidence that
linearly stable relative equilibria exist when the large and small circulation strengths are of the same sign, but that no
such solutions exist when they have opposite signs. The results of this paper are in contrast to those of the analogous celestial
mechanics problem, for which the N-gon is the only relative equilibrium for N sufficiently large, and is linearly stable if and only if N≥7. 相似文献
16.
We study the relationship between the generic smoothness of the Gauss map and the reflexivity (with respect to the projective dual) for a projective variety defined over an algebraically closed field. The problem we discuss here is whether it is possible for a projective variety X in ℙN to re‐embed into some projective space ℙM so as to be non‐reflexive with generically smooth Gauss map. Our result is that the answer is affirmative under the assumption that X has dimension at least 3 and the differential of the Gauss map of X in ℙN is identically zero; hence the projective varietyX re‐embedded in ℙM yields a negative answer to Kleiman–Piene's question: Does the generic smoothness of the Gauss map imply reflexivity for a projective variety? A Fermat hypersurface in ℙN with suitable degree in positive characteristic is known to satisfy the assumption above. We give some new, other examples of X in ℙN satisfying the assumption. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
I. L. Bloshanskii 《Analysis Mathematica》2000,26(2):81-98
The problem investigated is to characterize sets E, the sets of unbounded divergence (at each point) of single and multiple Fourier series under condition of convergence of these series to zero at each point of the complement of E.For any nonempty open set B T
N
= [0, 2]
N
, N 1, a Lebesgue integrable function f
0 is constructed which equals zero on the set U = T
N
\ B whose multiple trigonometric Fourier series diverges unboundedly (in the case of summation over squares) at each point of the set
, where
is the closure of the set
, pr(j)
is the orthogonal projection of the set
on the axis Ox
j
, j = 1,...,N. It is also proved that if
, then for any function f equal zero on the set U the multiple trigonometric Fourier series of the function f (in the case of summation over rectangles) converges at each point of the set T
N
\
. 相似文献
18.
Yury Orlovich Jacek Blazewicz Alexandre Dolgui Gerd Finke Valery Gordon 《Discrete Mathematics》2011,(16):1670
We consider the complexity of the maximum (maximum weight) independent set problem within triangle graphs, i.e., graphs G satisfying the following triangle condition: for every maximal independent set I in G and every edge uv in G−I, there is a vertex w∈I such that {u,v,w} is a triangle in G. We also introduce a new graph parameter (the upper independent neighborhood number) and the corresponding upper independent neighborhood set problem. We show that for triangle graphs the new parameter is equal to the independence number. We prove that the problems under consideration are NP-complete, even for some restricted subclasses of triangle graphs, and provide several polynomially solvable cases for these problems within triangle graphs. Furthermore, we show that, for general triangle graphs, the maximum independent set problem and the upper independent neighborhood set problem cannot be polynomially approximated within any fixed constant factor greater than one unless P=NP. 相似文献
19.
A two-component reaction–diffusion system modelling a class of spatially structured epidemic systems is considered. The system describes the spatial spread of infectious diseases mediated by environmental pollution. The internal zero stabilization is investigated. We provide necessary conditions of stabilizability and sufficient conditions of stabilizability. In the affirmative case a simple feedback stabilizing control is indicated. It shows that it is possible to diminish exponentially the epidemic process, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain (think globally, act locally). 相似文献
20.
We consider a model of a massless particle in a D-dimensional space with the Lagrangian proportional to the Nth extrinsic curvature of the world line. We present the Hamiltonian formulation of the system and show that its trajectories are spacelike curves satisfying the conditions k
N+a
=k
N-a and k
2N
=0, a=1,,N-1, where N[(D-2)/2]. The first N curvatures take arbitrary values, which is a manifestation of N+1 gauge degrees of freedom; the corresponding gauge symmetry forms an algebra of the W type. This model describes D-dimensional massless particles, whose helicity matrix has N coinciding nonzero weights, while the remaining [(D-2)/2]-N weights are zero. We show that the model can be extended to spaces with nonzero constant curvature. It is the only system with the Lagrangian dependent on the world-line extrinsic curvatures that yields irreducible representations of the Poincaré group. 相似文献