共查询到20条相似文献,搜索用时 32 毫秒
1.
O. I. Kocherha 《Nonlinear Oscillations》2007,10(2):246-256
We prove the asymptotic character of a solution of the Cauchy problem for a singularly perturbed linear system of differential
equations with degenerate matrix of the coefficients of derivatives in the case where the limit matrix pencil is regular and
has multiple “finite” and “infinite” elementary divisors. We establish conditions under which the constructed formal solutions
are asymptotic expansions of the corresponding exact solutions.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 247–257, April–June, 2007. 相似文献
2.
We consider a singularly perturbed system of differential equations with irregular singular point. We prove that, in the general
case of multiple elementary divisors, the corresponding asymptotic expansions can be constructed in the form of double series
in fractional powers of the parameter and the ratio of the independent variable to the parameter. 相似文献
3.
In this paper, we give a complete characterization of the asymptotic behaviour of solutions to the Navier–Stokes–Fourier system.
We show that either the driving force behaves asymptotically as a gradient of a scalar function, in which case any solution
tends to a static state, or the total energy goes to infinity with growing time. 相似文献
4.
Zh. L. Mal’tseva 《Journal of Applied Mechanics and Technical Physics》1999,40(5):824-830
Solitary waves on an interface between two fluids are considered. A uniform asymptotic expansion is constructed for internal
solitary waves with flat crests (of the plateau type) that degenerate into a bore in the limit. It is shown that, in this
case, in contrast to a Korteweg-de Vries wave, the wave amplitude is of the same order of smallness as the longwave approximation
parameter.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 55–61, September–October, 1999. 相似文献
5.
We propose an algorithm for the construction of an asymptotic solution of the Cauchy problem for a singularly perturbed linear
system of differential equations with degenerate matrix of coefficients of derivatives in the case where the limit pencil
of matrices is singular.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 271–288, April–June, 2008. 相似文献
6.
Dorin Bucur Eduard Feireisl Šárka Nečasová 《Journal of Mathematical Fluid Mechanics》2008,10(4):554-568
We consider a stationary Navier–Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming
the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional
to a small parameter ε, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system
of the Navier–Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary
conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is
allowed without any constraint.
The work of Š. N. supported by Grant IAA100190505 of GA ASCR in the framework of the general research programme of the Academy
of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503. 相似文献
7.
L. I. Karandjulov 《Nonlinear Oscillations》2008,11(1):44-54
We construct an asymptotic expansion of a solution for singularly perturbed linear systems of ordinary differential equations
of the Noether type in the critical case. We successively determine all terms of the asymptotic expansion by the method of
boundary functions and pseudoinverse matrices.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 1, pp. 45–54, January–March, 2007. 相似文献
8.
9.
N. V. Gnevanov B. L. Smorodin 《Journal of Applied Mechanics and Technical Physics》2006,47(2):214-220
Stability of a plane-parallel flow of a nonuniformly heated binary mixture filling a vertical layer located in a field of
gravity and in a high-frequency vibrational field is studied. The axis of vibrations is directed along the layer. The case
of rigid and isothermal boundaries of the layer impermeable for the mixture is considered. The influence of thermal diffusion
on the evolution of the admixture and the thresholds of flow stability is taken into account. The study is performed on the
basis of equations for averaged fields. An asymptotic method with the use of the perturbation wavenumber as a small parameter
is applied in the long-wave limit. For arbitrary values of the wavenumber, the limit of stability was determined by numerical
integration. Charts of stability of gaseous and liquid binary mixtures are plotted.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 77–84, March–April, 2006. 相似文献
10.
We investigate the asymptotic behavior of the general solution of the linear system of differential equations with irregular singular point
in the case where the limit matrix of the coefficients of the derivatives is degenerate. We deduce a branching equation whose coefficients contain complete information on the structure of the general solution of the system considered in the case of multiple finite and infinite elementary divisors of the regular pencil of matrices L() = A
0 – B
0. 相似文献
11.
P. F. Samusenko 《Nonlinear Oscillations》2008,11(3):427-441
We obtain an asymptotic solution of the Cauchy problem for a singularly perturbed degenerate system of differential equations
in the case of a singular limit pencil of matrices.
Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 408–420, July–September, 2008. 相似文献
12.
We investigate the Andronov-Hopf bifurcation of the birth of a periodic solution from a space-homogeneous stationary solution
of the Neumann problem on a disk for a parabolic equation with a transformation of space variables in the case where this
transformation is the composition of a rotation by a constant angle and a radial contraction. Under general assumptions, we
prove a theorem on the existence of a rotating structure, deduce conditions for its orbital stability, and construct its asymptotic
form.
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Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 155–169, April–June, 2006. 相似文献
13.
S. B. Kozitskii 《Journal of Applied Mechanics and Technical Physics》2000,41(3):429-438
The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the
neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex Ginzburg-Landau
equation, a Newell-Whitehead-type equation, and an equation of the ϕ4 type, respectively, were obtained. Analytic expressions for the coefficients of these equations and their various asymptotic
forms are presented. In the case of Hopf bifurcation for low and high frequencies, the amplitude equation reduces to a perturbed
nonlinear Shroedinger equation. In the high-frequency limit, structures of the type of “dark” solitons are characteristic
of the examined physical system.
Pacific Ocean Institute, Vladivostok 690041. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3,
pp. 56–66, May–June, 2000. 相似文献
14.
Sergey A. Nazarov Iryna L. Pankratova Andrey L. Piatnitski 《Archive for Rational Mechanics and Analysis》2011,200(3):747-788
The paper deals with the asymptotic behaviour of spectra of second order self-adjoint elliptic operators with periodic rapidly
oscillating coefficients in the case when the density function (the factor on the spectral parameter) changes sign. We study
the Dirichlet problem in a regular bounded domain and show that the spectrum of this problem is discrete and consists of two
series, one of them tending towards +∞ and another towards −∞. The asymptotic behaviour of positive and negative eigenvalues
and their corresponding eigenfunctions depends crucially on whether the average of the weight function is positive, negative
or equal to zero. We construct the asymptotics of eigenpairs in all three cases. 相似文献
15.
We study the boundary-layer approximation of the classical mathematical model that describes the discharge of a laminar hot
gas in a stagnant colder atmosphere of the same gas. We prove the existence and uniqueness of solutions to a nondegenerate
problem (without zones of stagnation of gas temperature or velocity). The asymptotic behavior of these solutions is also studied
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 192–205, July–August, 2008. 相似文献
16.
We consider a mixed boundary-value problem for the Poisson equation in a plane thick junction Ωε that is the union of a domain Ω0 and a large number of ε-periodically located thin rods. The nonuniform Signorini conditions are given on the vertical sides
of the thin rods. The asymptotic analysis of this problem is made as ε → 0, i.e., in the case where the number of thin rods
infinitely increases and their thickness tends to zero. With the help of the integral identity method, we prove the convergence
theorem and show that the nonuniform Signorini conditions are transformed (as ε → 0) into the limiting variational inequalities
in the domain that is filled up with thin rods when passing to the limit. The existence and uniqueness of a solution to this
nonstandard limit problem are established. The convergence of the energy integrals is proved as well.
Published in Neliniini Kolyvannya, Vol. 12, No. 1, pp. 44–58, January–March, 2009. 相似文献
17.
S. A. Nazarov 《Journal of Applied Mechanics and Technical Physics》2007,48(6):861-870
Explicit presentations for the initial terms of the asymptotic solution of the spectral problem of the elasticity theory in
a plane region with a rapidly oscillating boundary are obtained. Based on asymptotic formulas, two methods for problem modeling
are proposed: with the use of Wenzel’s boundary conditions and with the use of the principle of a smooth image of a singularly
perturbed boundary. Various approaches to justification of asymptotic presentations are discussed.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 103–114, November–December, 2007. 相似文献
18.
We study the low Mach number asymptotic limit for solutions to the full Navier–Stokes–Fourier system, supplemented with ill-prepared
data and considered on an arbitrary time interval. Convergencetowards the incompressible Navier–Stokes equations is shown. 相似文献
19.
We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory
coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to zero, this solution converges
to a solution of a sharp interface model, which describes the phase interface in an elastically deformable solid moving by
interface diffusion. Therefore, the coupled system can be used as diffusive interface model. Differently from diffusive interface
models based on the Cahn–Hilliard equation, the interface diffusion is solely driven by the bulk energy, hence the Laplacian
of the curvature is not part of the driving force. Also, no rescaling of the parabolic equation is necessary. Since the asymptotic
solution does not solve the system exactly, the proof is formal. 相似文献
20.
In this article, we study the large time behavior of solutions of first-order Hamilton–Jacobi Equations set in a bounded domain
with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence
results for viscosity solutions of these Cauchy–Neumann problems by using two fairly different methods: the first one relies
only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the
second one is an optimal control/dynamical system approach, named the “weak KAM approach”, which requires the convexity of
Hamiltonians and gives formulas for asymptotic solutions based on Aubry–Mather sets. 相似文献