共查询到20条相似文献,搜索用时 595 毫秒
1.
F. F. Fatykhov 《Journal of Mathematical Sciences》1993,65(1):1440-1445
The dynamics of an object-parachute system are examined with allowance for canopy pulsations. The law for the variation of the parachute's resistance is assumed to be harmonic. By means of the asymptotic method of nonlinear mechanics the equations for perturbed motion of the system with variable coefficients were investigated. Conditions were obtained for which the system has a parametric resonance. It is shown that in this case the amplitude of oscillations by the object-parachute system increases according to an exponential law.Translated from Dinamicheskie Sistemy, No. 5, pp. 67–73, 1986. 相似文献
2.
We propose a system of first-order equations of motion all solutions of which are solutions of a system of second-order equations of motion for the supersymmetric Yang–Mills theory with a scalar multiplet. We find N = 1 transformations under which the systems of first- and second-order equations of motion are invariant. 相似文献
3.
We study the unique solvability in the large on the semiaxis ℝ+ of the initial boundary value problems (IBVP) with the boundary slipcondition (the natural boundary condition) for the ɛ-approximations
(0.6)–(0.8), (0.20); (0.13)–(0.15), (0.21), and (0.16–0.18), (0.22) of the Navier-Stokes equations (NSE), of the NSE modified
in the sense of O. A. Ladyzhenskaya, and the equations of motion of the Kelvin-Voight fluids. For the classical solutions
of perturbed problems we prove certain estimates which are uniform with respect to ɛ, and show that as ɛ→0 the classical solutions
of the perturbed IBVP respectively converge to the classical solutions of the IBVP with the boundary slip condition for the
NSE, for the NSE (0.11) modified in the sense of Ladyzhenskaya, and for the equations (0.12) of motion of the Kelvin-Voight
fluids. Bibliography: 40 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 205, 1993, pp. 38–70.
Translated by A. P. Oskolkov. 相似文献
4.
The mathematical model considered here of a neuron system is a chain of an arbitrary number m ≥ 2 of diffusion-coupled singularly perturbed nonlinear delay differential equations with Neumann-type conditions at the
endpoints. We study the existence, asymptotic behavior, and stability of relaxation periodic solutions of this system. 相似文献
5.
Adrian Constantin 《Annali di Matematica Pura ed Applicata》1995,168(1):237-299
In this paper we consider sufficient conditions for the continuability of solutions for perturbed differential equations. We obtain also some results for the global existence of solutions for differential inclusions and for stochastic differential equations of McShane and Ito type. We give an application to the global inversion of local diffeomorphisms. 相似文献
6.
Caidi Zhao 《Mathematical Methods in the Applied Sciences》2013,36(7):840-856
This paper studies the approximation of the non‐Newtonian fluid equations by the artificial compressibility method. We first introduce a family of perturbed compressible non‐Newtonian fluid equations (depending on a positive parameter ε) that approximates the incompressible equations as ε → 0+. Then, we prove the unique existence and convergence of solutions for the compressible equations to the solutions of the incompressible equations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
A. A. Chesnokov 《Journal of Applied and Industrial Mathematics》2010,4(1):24-34
We consider a system of nonlinear differential equations which describes the spatial motion of an ideal incompressible fluid
on a rotating plane in the shallow water approximation and a more general system of the theory of long waves which takes into
account the specifics of shear flows. Using the group analysis methods, we calculate the 9-dimensional Lie algebras of infinitesimal
operators admissible by the models. We establish an isomorphism of these Lie algebras with a known Lie algebra of operators
admissible by the system of equations for the two-dimensional isentropic motions of a polytropic gas with the adiabatic exponent
γ = 2. The nontrivial symmetries of the models under consideration enable us to carry out the group generation of the solutions.
The class of stationary solutions to the equations of rotating shallow water transforms into a new class of periodic solutions. 相似文献
8.
We consider the planar rotation-symmetric motion by inertia of a viscous incompressible fluid in a ring with free boundary. We reduce the corresponding initial-boundary value problem for the Navier–Stokes equations to some problem for a coupled system of one parabolic equation and two ordinary differential equations. We suppose that the coefficient of the derivatives of the sought functions with respect to time (the quasistationary parameter) is small; so the system is singularly perturbed. In this article we construct an asymptotic expansion for a solution to the rotating ring problem in a small quasistationary parameter and obtain a smallness estimate for the difference between the exact and approximate solutions. 相似文献
9.
A. N. Andronov 《Differential Equations》2011,47(5):758-763
We study the stability of branching solutions of a system of two nonlinearly perturbed Laplace equations in a half-space with
two differential relations on the interface. This system describes the motion of a two-layer fluid. To construct and study
the related branching systems, methods of group analysis of differential equations (RZhMat 1978 11B883K, RZhMat 1983 11A813K)
and the S. Lie-L.V. Ovsyannikov technique of invariants and invariant manifolds are used. 相似文献
10.
A. S. Makarenko 《Journal of Mathematical Sciences》1994,70(1):1529-1533
Problems in the mathematical modeling of heat-distribution processes on the basis of more general equations than parabolic equations are considered. We study the general structure of the relations between solutions of various approximations to the generalized heat-conductivity equations. We introduce a notion of singularly perturbed dissipative structures and analyze singularly perturbed blow-up regimes.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 70, pp. 54–60, 1990. 相似文献
11.
In a previous paper, the authors suggested a procedure for obtaining all solutions to certain systems ofn equations inn complex variables. The idea was to start with a trivial system of equations to which all solutions were easily known. The trivial system was then perturbed into the given system. During the perturbation process, one followed the solution paths from each of the trivial solutions into the solutions of the given system. All solutions to the given system were thereby obtained.This paper utilizes a different approach that eliminates the requirement of the previous paper for a leading dominating term in each equation. We add a dominating term artificially and then fade it. Also we rely on mathematically more fundamental concepts from differential topology. These advancements permit the calculation of all solutions to arbitrary polynomials and to various other systems ofn equations inn complex variables. In addition, information on the number of solutions can be obtained without calculation.Work supported in part by NSF Grant No. MCS77-15509 and ARO Grant No. DAAG-29-78-G-0160.Work supported in part by ARO Grant No. DAAG-29-78-G-0160 相似文献
12.
The Perron effect is the effect in which the characteristic Lyapunov exponents of solutions of a differential system change
sign from negative to positive when passing to a perturbed system. We show that this effect is realized on all nontrivial
solutions of two two-dimensional systems: an original linear system with negative characteristic exponents and a perturbed
system with small perturbations of arbitrary order m > 1 in a neighborhood of the origin, all of whose nontrivial solutions have positive characteristic exponents. We compute
the exact positive value of the characteristic exponents of solutions of the two-dimensional nonlinear Perron system with
small second-order perturbations, which realizes only a partial Perron effect. 相似文献
13.
Any solution of the functional equation
where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an α-perturbed
reflected Brownian motion. Similarly any solution of
behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an α,β-doubly perturbed Brownian
motion. We complete some recent investigations by showing that for all permissible values of the parameters α, α and β respectively,
these equations have pathwise unique solutions, and these are adapted to the filtration of B.
Received: 7 November 1997 / Revised version: 13 July 1998 相似文献
14.
《随机分析与应用》2013,31(6):1281-1307
The paper is devoted to the generalized stochastic differential equations of the Ito? type whose coefficients are additionally perturbed and dependent on a small parameter. Their solutions are compared with the solutions of the corresponding unperturbed equations. We give conditions under which the solutions of these equations are close in the (2m)-th moment sense on finite intervals or on intervals whose length tends to infinity as the small parameter tends to zero. We also give the degree of the closeness of these solutions. 相似文献
15.
Summary Two related systems of coupled modulation equations are studied and compared in this paper. The modulation equations are derived
for a certain class of basic systems which are subject to two distinct, interacting, destabilising mechanisms. We assume that,
near criticality, the ratio of the widths of the unstable wavenumber-intervals of the two (weakly) unstable modes is small—as,
for instance, can be the case in double-layer convection. Based on these assumptions we first derive a singularly perturbed
modulation equation and then a modulation equation with a nonlocal term. The reduction of the singularly perturbed system
to the nonlocal system can be interpreted as a limit in which the width of the smallest unstable interval vanishes. We study
and compare the behaviour of the stationary solutions of both systems. It is found that spatially periodic stationary solutions
of the nonlocal system exist under the same conditions as spatially periodic stationary solutions of the singularly perturbed
system. Moreover, these solutions can be interpreted as representing the same quasi-periodic patterns in the underlying basic
system. Thus, the ‘Landau reduction’ to the nonlocal system has no significant influence on the stationary quasi-periodic
patterns. However, a large variety of intricate heteroclinic and homoclinic connections is found for the singularly perturbed
system. These orbits all correspond to so-called ‘localised structures’ in the underlying system: They connect simple periodic
patterns atx → ± ∞. None of these patterns can be described by the nonlocal system. So, one may conclude that the reduction to the nonlocal
system destroys a rich and important set of patterns. 相似文献
16.
Yeping Li 《Mathematical Methods in the Applied Sciences》2005,28(16):1955-1975
We investigate a multi‐dimensional isentropic hydrodynamic (Euler–Poisson) model for semiconductors, where the energy equation is replaced by the pressure–density relation p(n) . We establish the global existence of smooth solutions for the Cauchy–Neumann problem with small perturbed initial data and homogeneous Neumann boundary conditions. We show that, as t→+∞, the solutions converge to the non‐constant stationary solutions of the corresponding drift–diffusion equations. Moreover, we also investigate the existence and uniqueness of the stationary solutions for the corresponding drift–diffusion equations. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
17.
K. M. Ramachandran 《随机分析与应用》2013,31(4):710-723
Abstract Stochastic delay differential equations with wideband noise perturbations is considered. First it is shown that the perturbed system converges weakly to a stochastic delay differential equation driven by a Brownian motion. Stability and asymptotic properties of stochastic delay differential equations with a small parameter are developed. It is shown that the properties such as stability, recurrence, etc., of the limit system with time lag is preserved for the solution x ?(·) of the underlying delay equation for ? > 0 small enough. Perturbed Liapunov function method is used in the analysis. 相似文献
18.
For the set of equations of perturbed motion whose solutions satisfy interval initial conditions, we obtain sufficient conditions for the Lyapunov stability and the practical stability of these solutions. The analysis is performed on the basis of locally large scalar Lyapunov functions. As examples, we consider quasilinear and linear nonautonomous systems. 相似文献
19.
20.
We provide necessary and sufficient conditions for the existence of T-periodic solutions of a system of second-order ordinary differential equations that models the motion of two or three collinear charged particles of the same sign. 相似文献