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661.
P. De Maesschalck 《Journal of Differential Equations》2008,244(6):1448-1466
This paper deals with the smoothness of the transition map between two sections transverse to the fast flow of a singularly perturbed vector field (one fast, multiple slow directions). Orbits connecting both sections are canard orbits, i.e. they first move rapidly towards the attracting part of a critical surface, then travel a distance near this critical surface, even beyond the point where the orbit enters the repelling part of the critical surface, and finally repel away from the surface. We prove that the transition map is smooth. In a transcritical situation however, where orbits from an attracting part of one critical manifold follow the repelling part of another critical manifold, the smoothness of the transition map may be limited, due to resonance phenomena that are revealed by blowing up the turning point! We present a polynomial example in R3. 相似文献
662.
Hossein Tehrani 《Journal of Differential Equations》2007,236(1):1-28
We study existence results for a nonlinear Schrödinger equation at resonance. The nonlinearity is assumed to change sign, be unbounded but sublinear with a power like growth at infinity. Under a suitable coercivity assumption on the primitive of the nonlinear term on the kernel of the Schrödinger operator, we prove the existence of at least one solution. 相似文献
663.
M. M. Lavrent’ev V. I. Maksimov 《Computational Mathematics and Mathematical Physics》2008,48(4):641-647
A parabolic equation under the influence of external perturbations is considered. It is assumed that the solutions to this equation are measured (possibly with errors). The problem of construction of differential equations for estimation (reconstruction) of perturbations using the measured data is discussed. Differential equations of the auxiliary system whose right-hand sides are approximations of the unknown input are derived. 相似文献
664.
Sergey S. Kokarev 《General Relativity and Gravitation》2009,41(8):1777-1794
Cosmological singularity and asymptotic behavior of scale factor of generalized cosmological models are analyzed in respect
of their structural stability. It is shown, that cosmological singularity is structurally unstable for the majority of models
with barotropic perfect fluid with strong energy condition. Inclusion of Λ-term extends the set of structurally stable cosmological
models. 相似文献
665.
吴晓非 《数学物理学报(A辑)》2001,21(1):1-7
该文应用大系统的分解方法及一个推广的不等式,研究了一类时变大系统在结构扰动下的平稳振荡问题,得到了一些新结果. 相似文献
666.
This paper studies a low order mixed finite element method (FEM) for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q 1 rot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H 1-norm and the pressure in the L 2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results. 相似文献
667.
Leonid Berezansky Michael Gil&rsquo & Liora Troib 《advances in applied mathematics and mechanics.》2011,3(5):562-571
The paper deals with periodic systems of ordinary differential equations (ODEs).
A new approach to the investigation of variations of multipliers under
perturbations is suggested. It enables us to establish explicit conditions for the stability and instability of perturbed systems. 相似文献
668.
M. S. Kotel’nikova B. A. Lugovtsov 《Journal of Applied Mechanics and Technical Physics》2009,50(2):243-250
This paper considers the problem of the evolution of azimuthal perturbations in axisymmetric magnetohydrodynamic. flows of
an ideally conducting inviscid fluid with circular streamlines. The fluid is. in a toroidal gap between two surfaces with
constant values of the stream function. The equations of. fluid motion are derived in the approximation of infinitely a narrow
gap. The parameters at which. spontaneous swirling is possible are determined numerically, and the properties of secondary
swirling. flows resulting from instability of the initial steady-state poloidal flow are established.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 89–97, March–April, 2009. 相似文献
669.
M.B.A.Mansour 《应用数学和力学(英文版)》2009,30(4):513-516
In this paper, we consider a dissipative-dispersive nonlinear equation appliable to many physical phenomena. Using the geometric singular perturbation method based on the theory of dynamical systems, we investigate the existence of its traveling wave solutions with the dissipative terms having sufficiently small coefficients. The results show that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ordinary differential equations (ODEs). Then, we use the Melnikov method to establish the existence of a homoclinic orbit in this manifold corresponding to a solitary wave solution of the equation. Furthermore, we present some numerical computations to show the approximations of such wave orbits. 相似文献
670.
Shaohong Cai 《Nonlinear dynamics》2009,57(3):375-382
In this paper, we study a stage-structured single species model with pulse input in a polluted environment. Using the discrete
dynamical system determined by the stroboscopic map, we obtain the globally attractive condition for the species-extinction
periodic solution of the investigated system. By the use of the theory of impulsive delayed differential equation, we also
obtain sufficient condition of the permanence of the investigated system. Our results reveal that long mature period of the
population in polluted environment can cause it to go extinct.
Supported by National Natural Science Foundation of China (10647005), and the Nomarch Foundation of Guizhou Province. 相似文献