共查询到20条相似文献,搜索用时 265 毫秒
1.
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.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 103–114, November–December, 2007. 相似文献
2.
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.
__________
Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 247–257, April–June, 2007. 相似文献
3.
Jens Rottmann-Matthes 《Journal of Dynamics and Differential Equations》2012,24(2):341-367
It is a well-known problem to derive nonlinear stability of a traveling wave from the spectral stability of a linearization.
In this paper we prove such a result for a large class of hyperbolic systems. To cope with the unknown asymptotic phase, the
problem is reformulated as a partial differential algebraic equation for which asymptotic stability becomes usual Lyapunov
stability. The stability proof is then based on linear estimates from (Rottmann-Matthes, J Dyn Diff Equat 23:365–393, 2011) and a careful analysis of the nonlinear terms. Moreover, we show that the freezing method (Beyn and Thümmler, SIAM J Appl
Dyn Syst 3:85–116, 2004; Rowley et al. Nonlinearity 16:1257–1275, 2003) is well-suited for the long time simulation and numerical approximation of the asymptotic behavior. The theory is illustrated
by numerical examples, including a hyperbolic version of the Hodgkin–Huxley equations. 相似文献
4.
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
5.
A. P. Krenevych 《Nonlinear Oscillations》2006,9(2):207-214
We investigate the problem of the asymptotic equivalence of systems of nonlinear ordinary and stochastic equations in mean
square and with probability one.
__________
Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 213–220, April–June, 2006. 相似文献
6.
S. E. Selezneva 《Fluid Dynamics》1998,33(4):630-632
The range of applicability of the asymptotic solution of the problem of incompressible flow past a slender cone is studied.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 197–200, July–August, 1998. 相似文献
7.
Sebastian Bönisch Vincent Heuveline Peter Wittwer 《Journal of Mathematical Fluid Mechanics》2008,10(1):45-70
We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain
in two dimensions. For numerical purposes we truncate the domain to a finite sub-domain, which leads to the problem of finding
so called “artificial boundary conditions” to replace the boundary conditions at infinity. To solve this problem we construct
– by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of
Goldstein and Van Dyke – a smooth divergence free vector field depending explicitly on drag and lift and describing the solution
to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be
new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to
non-symmetric flows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent
way as an integral part of the solution process. When compared with our previous paper where first order asymptotic expressions
were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost
for determining lift and drag to a given precision by typically another order of magnitude.
Peter Wittwer: Supported in part by the Fonds National Suisse. 相似文献
8.
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.
__________
Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 271–288, April–June, 2008. 相似文献
9.
A. Ya. Voronov 《Fluid Dynamics》1998,33(3):450-458
An asymptotic representation for the solution of the problem of the radial structure of the internal boundary (transition)
layer and the radial distribution of the basic physical plasma characteristics of the column of a free-burning low-pressure
electric are in He is constructed.
Sarov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–195, May–June, 1998. 相似文献
10.
V. A. Khandogin 《Journal of Applied Mechanics and Technical Physics》1998,39(3):467-475
The elastic equilibrium of an isotropic plane with one linear defect under conditions of longitudinal shear is considered.
The strain field is constructed by the solution of a twodimensional boundary-value Riemann problem with variable coefficients.
A special method that reduce the general two-dimensional problem to two one-dimensional problems is proposed. The strain field
is described by three types of asymptotic relations: for the tups of the defect, for the tips of the reinforcing edge, and
also at a distance from the closely spaced tips of the defect and the rib. The general form of asymptotic relations for strains
with finite energy is deduced from analysis of the variational symmetries of the equations of longitudinal shear. A paradox
of the primal mixed boundary-value problem for cracks is formulated and a method of solving the problem is proposed.
Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika,
Vol. 39, No. 3, pp. 163–172, May–June, 1998. 相似文献
11.
V. A. Chugunov L. D. Eskin S. L. Tonkonog 《Journal of Applied Mechanics and Technical Physics》2000,41(2):267-272
The problem of exhaustion of a thin film of a non-Newtonian fluid with a power rheological law from a slotted orifice is solved
with account of film slipping relative to the underlying surface. By the method of group analysis with transformation of the
parameters entering the problem, an asymptotic formula for the film profile is obtained and a law of motion of the film edge
with small slipping is derived.
Kazan' State University, 420008 Kazan'. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp.
71–76, March–April, 2000. 相似文献
12.
I. I. Argatov 《Journal of Applied Mechanics and Technical Physics》2008,49(1):98-104
An asymptotic model for deformation of an elastic space with a rigid thin reinforcing bar is constructed. The elastic modulus
of the fiber far exceeds the elastic modulus of the matrix. The shape optimization problem for the reinforcing bar is solved
on the basis of the uniform strength condition.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 120–128, January–February, 2008. 相似文献
13.
V. M. Shapovalov 《Journal of Applied Mechanics and Technical Physics》2006,47(2):199-207
An asymptotic analysis of the plane problem of reptation motion of animals in a fluid is performed in a long-wave approximation.
Turbulent motion is considered. Asymptotic estimates are obtained for the axial and shear forces, expended energy, and motion
trajectory. Results of numerical analysis are given.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 60–69, March–April, 2006. 相似文献
14.
A. G. Kolpakov 《Journal of Applied Mechanics and Technical Physics》1998,39(4):611-617
Variational principles and estimates (including two-sided estimates) are obtained for the rigidities of bodies containing
periodic systems of pores (voids). The problem is examined on the basis of the asymptotic averaging method.
Siberian State Academy of Telecommunications and Informatics, Novosibirsk 630009. Translated from Prikladnaya Mekhanika i
Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 148–154, July–August, 1998. 相似文献
15.
For a second-order symmetric uniformly elliptic differential operator with rapidly oscillating coefficients, we study the
asymptotic behavior of solutions of a mixed inhomogeneous boundary-value problem and a spectral Neumann problem in a thin
perforated domain with rapidly varying thickness. We obtain asymptotic estimates for the differences between solutions of
the original problems and the corresponding homogenized problems. These results were announced in Dopovidi Akademii Nauk Ukrainy, No. 10, 15–19 (1991). The new results obtained in the present paper are related to the construction of an asymptotic expansion
of a solution of a mixed homogeneous boundary-value problem under additional assumptions of symmetry for the coefficients
of the operator and for the thin perforated domain. 相似文献
16.
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
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 192–205, July–August, 2008. 相似文献
17.
V. P. Ryabchenko 《Journal of Applied Mechanics and Technical Physics》2008,49(2):267-276
This paper considers a two-dimensional linear unsteady problem of rigid-stamp indentation on an elastic layer of finite thickness
lying on the surface of a compressible fluid of infinite depth. The Lamé equations holds for the elastic layer, and the wave
equation for the fluid velocity potential. Using the Laplace and Fourier transforms, the problem is reduced to determining
the contact stresses under the stamp from the solution of an integral equation of the first kind, whose kernel has a logarithmic
singularity. An asymptotic solution of the problem is constructed for large times of interaction.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 131–142, March–April, 2008. 相似文献
18.
We study free oscillations of a viscous incompressible fluid with free boundary in a hemispherical tank. We determine four
systems of coordinate functions that satisfy the equations of the problem inside the domain and possess the properties of
the required solution. Then, using these systems, we construct a coordinate system that satisfies all but one boundary condition
of the problem. This system is used for the solution of the problem by a projection method. We compute the eigenfrequencies
and logarithmic decrements of oscillations of the fluid. The results obtained are compared with asymptotic and empirical formulas.
Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 439–461, October–December, 2008. 相似文献
19.
A. M. Khludnev 《Journal of Applied Mechanics and Technical Physics》2008,49(4):553-567
The contact problem for two elastic plates aligned at a prescribed angle to each other is considered. The set of contact points
is assumed to be unknown in advance and to be determined only after the problem is solved. Various formulations of the problem
are given, and their equivalence is proved. A complete set of boundary conditions fulfilled on the contact domain is found,
and the character of satisfaction of these conditions is described. The asymptotic properties of solutions are studied for
rigidity parameters of the contacting plates tending to infinity.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 42–58, July–August, 2008. 相似文献
20.
N. V. Khusnutdinova 《Journal of Applied Mechanics and Technical Physics》1999,40(3):386-392
The asymptotic behavior (with unlimited increase in time) of solutions of boundary-value problems for the filtration equation
for a two-phase liquid that describe the displacement of immiscible incompressible liquids from a bed is studied. Convergence
of these solutions to the unique solution of the steady problem (stabilization) is established, and, under additional assumptions,
the rate of convergence is evaluated.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 30–36, May–JJune, 1999. 相似文献