共查询到20条相似文献,搜索用时 46 毫秒
1.
E. F. Lelikova 《Proceedings of the Steklov Institute of Mathematics》2013,281(1):95-104
We study the asymptotic behavior of a solution of the first boundary value problem for a second-order elliptic equation in a nonconvex domain with smooth boundary in the case where a small parameter is a factor at only some of the highest derivatives and the limit equation is an ordinary differential equation. Although the limit equation has the same order as the initial equation, the problem is singulary perturbed. The asymptotic behavior of its solution is studied by the method of matched asymptotic expansions. 相似文献
2.
S. I. Mitrokhin 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):184-193
The aim of this paper is to study spectral properties of differential operators with integrable coefficients and a constant
weight function. We analyze the asymptotic behavior of solutions to a differential equation with integrable coefficients for
large values of the spectral parameter. To find the asymptotic behavior of solutions, we reduce the differential equation
to a Volterra integral equation. We also obtain asymptotic formulas for the eigenvalues of some boundary value problems related
to the differential operator under consideration. 相似文献
3.
M. S. Sgibnev 《Siberian Mathematical Journal》2012,53(6):1139-1154
We obtain an asymptotic expansion for a solution to an mth order nonhomogeneous differential-difference equation of retarded or neutral type. Account is taken of the influence of the roots of the characteristic equation. The exact asymptotics of the remainder is established depending on the asymptotic properties of the free term of the equation. 相似文献
4.
J. J. H. Brouwers 《Theoretical and Mathematical Physics》2010,163(2):677-695
We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-induced turbulence (turbulent
flow in pipes, channels, and boundary layers including the atmospheric surface layer). The analysis is based on the asymptotic
behavior at a large Reynolds number. We use the Lagrangian Kolmogorov theory, recently derived asymptotic expressions for
the spatial distribution of turbulent energy dissipation, and also newly derived reciprocity relations analogous to the Onsager
relations supplemented with recent measurement results. The long-time limit of the derived Langevin equation yields the diffusion
equation for admixture dispersion in wall-induced turbulence. 相似文献
5.
韩忠月 《数学的实践与认识》2009,39(7)
讨论了循环序列x_(n+1)=(α-βx_n)/(γ+x_(n-1)),n=0,1,2,….解的整体渐近稳定性,用系数α,β,γ给出了其正的平衡点是全局吸引的充分条件及全局吸引域.其中α,β,γ为正实数. 相似文献
6.
We study the initial value problem of a singularly perturbed first order ordinary differential equation in case that the degenerate equation has a double root. We construct the formal asymptotic expansion of the solution such that the boundary layer functions decay exponentially. This requires a modification of the standard procedure. The asymptotic solution will be used to construct lower and upper solutions guaranteeing the existence of a unique solution and justifying its asymptotic expansion. 相似文献
7.
The purpose of this article is to perform an asymptotic analysis for an interaction problem between a viscous fluid and an elastic structure when the flow domain is a three-dimensional cylindrical tube. We consider a periodic, non-steady, axisymmetric, creeping flow of a viscous incompressible fluid through a long and narrow cylindrical elastic tube. The creeping flow is described by the Stokes equations and for the wall displacement we consider the Koiter's equation. The well posedness of the problem is proved by means of its variational formulation. We construct an asymptotic approximation of the problem for two different cases. In the first case, the stress term in Koiter's equation contains a great parameter as a coefficient and dominates with respect to the inertial term while in the second case both the terms are of the same order and contain the great parameter. An asymptotic analysis is developed with respect to two small parameters. Analysing the leading terms obtained in the second case, we note that the wave phenomena takes place. The small error between the exact solution and the asymptotic one justifies the below constructed asymptotic expansions. 相似文献
8.
In this paper, we study a general multidimensional nonisentropic hydrodynamical model for semiconductors. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. For steady state, subsonic and potential flows, we discuss the zero-electron-mass limit of system by using the method of asymptotic expansions. We show the existence and uniqueness of profiles, and justify the asymptotic expansions up to any order. 相似文献
9.
We prove a non-equilibrium functional central limit theorem for the position of a tagged particle in mean-zero one-dimensional zero-range process. The asymptotic behavior of the tagged particle is described by a stochastic differential equation governed by the solution of the hydrodynamic equation. 相似文献
10.
M. V. Komarov 《Differential Equations》2011,47(12):1726-1745
We study conditions for the existence of a solution of a periodic problem for a model nonlinear equation in the spatially multidimensional case and consider various types of large time asymptotics (exponential and oscillating) for such solutions. The generalized Kolmogorov-Petrovskii-Piskunov equation, the nonlinear Schrödinger equation, and some other partial differential equations are special cases of this equation. We analyze the solution smoothing phenomenon under certain conditions on the linear part of the equation and study the case of nonsmall initial data for a nonlinearity of special form. The leading asymptotic term is presented, and the remainder in the asymptotics of the solution is estimated in a spatially uniform metric. 相似文献
11.
Waves with constant, nonzero linearized frequency form an interesting class of nondispersive waves whose properties differ from those of nondispersive hyperbolic waves. We propose an inviscid Burgers‐Hilbert equation as a model equation for such waves and give a dimensional argument to show that it models Hamiltonian surface waves with constant frequency. Using the method of multiple scales, we derive a cubically nonlinear, quasi‐linear, nonlocal asymptotic equation for weakly nonlinear solutions. We show that the same asymptotic equation describes surface waves on a planar discontinuity in vorticity in two‐dimensional inviscid, incompressible fluid flows. Thus, the Burgers‐Hilbert equation provides an effective equation for these waves. We describe the Hamiltonian structure of the Burgers‐Hilbert and asymptotic equations, and show that the asymptotic equation can also be derived by means of a near‐identity transformation. We derive a semiclassical approximation of the asymptotic equation and show that spatially periodic, harmonic traveling waves are linearly and modulationally stable. Numerical solutions of the Burgers‐Hilbert and asymptotic equations are in excellent agreement in the appropriate regime. In particular, the lifespan of small‐amplitude smooth solutions of the Burgers‐Hilbert equation is given by the cubically nonlinear timescale predicted by the asymptotic equation. © 2009 Wiley Periodicals, Inc. 相似文献
12.
Olof J Staffans 《Journal of Differential Equations》1977,24(3):365-382
We consider the asymptotic behavior of the bounded solutions of a nonlinear Volterra integrodifferential equation with a positive definite convolution kernel. Our main result states that (under appropriate assumptions) the asymptotic spectra of the solutions are contained in the set where the real part of the Fourier transform of the kernel vanishes. We also give a new asymptotic stability theorem, and present a new proof of a known result on the asymptotic behavior of the bounded solutions of a nonlinear, nondifferentiated Volterra equation. 相似文献
13.
A. A. Pozharskii 《Theoretical and Mathematical Physics》2006,146(3):343-360
We study the Schrödinger equation describing the one-dimensional motion of a quantum electron in a periodic crystal placed in an accelerating electric field. We describe the asymptotic behavior of equation solutions at large values of the argument. Analyzing the obtained asymptotic expressions, we present rather loose conditions on the potential under which the spectrum of the corresponding operator is purely absolutely continuous and spans the entire real axis. 相似文献
14.
N. A. Sidorov D. N. Sidorov R. Yu. Leont’ev 《Journal of Applied and Industrial Mathematics》2012,6(3):387-392
We consider a nonlinear operator equation with a Fredholm linear operator in the principal part. The nonlinear part of the equation depends on the functionals defined on an open set in a normed vector space. We propose a method of successive asymptotic approximations to branching solutions. The method is used for studying the nonlinear boundary value problem describing the oscillations of a satellite in the plane of its elliptic orbit. 相似文献
15.
Ikki Fukuda 《Mathematical Methods in the Applied Sciences》2020,43(8):5532-5563
We consider the large time asymptotic behavior of the global solutions to the initial value problem for the nonlinear damped wave equation with slowly decaying initial data. When the initial data decay fast enough, it is known that the solution to this problem converges to the self-similar solution to the Burgers equation called a nonlinear diffusion wave, and its optimal asymptotic rate is obtained. In this paper, we focus on the case that the initial data decay more slowly than previous works and derive the corresponding asymptotic profile. Moreover, we investigate how the change of the decay rate of the initial values affect its asymptotic rate. 相似文献
16.
In this work we consider the first boundary value problem for a parabolic equation of second order with a small parameter on a half-axis (i.e., we consider the one-dimensional case). We take the zero initial condition. We construct the global (that is, the caustic points are taken into account) asymptotics of a solution for the boundary value problem. The asymptotic solution of this problem has a different structure depending on the sign of the coefficient (the drift coefficient) at the derivative of first order at a boundary point. The constructed asymptotic solutions are justified. 相似文献
17.
研究Boltzmann方程的一个动力学模型:Tjon-Wu方程的更一般的形式.我们证明了在L_(1.1)范数意义下方程的稳态解的渐近稳定性. 相似文献
18.
V. F. Butuzov 《Differential Equations》2015,51(12):1569-1582
We construct and justify the asymptotics of a boundary layer solution of a boundary value problem for a singularly perturbed second-order ordinary differential equation for the case in which the degenerate (finite) equation has an identically double root. A specific feature of the asymptotics is the presence of a three-zone boundary layer. The solution of the boundary value problem is a stationary solution of the corresponding parabolic equation. We prove the asymptotic stability of this solution and find its attraction domain. 相似文献
19.
A. A. Pozharskii 《Journal of Mathematical Sciences》2009,156(4):669-698
We study the adiabatic asymptotics of reflection coefficients of a quantum electron moving in a two-dimensional waveguide.
The direction of the waveguide axis can slowly change, whereas the cut-section is a periodic function slowly varying along
the waveguide axis. The motion of an electron is described by the free Helmoltz equation. We study turning points in a neighborhood
of which considerable reflection of an electron is observed. We describe the asymptotic behavior of reflection coefficients
and uniform asymptotic formulas for the wave function of electron; moreover, these formulas remain valid even if the turning
points approach each other. An example of a waveguide with four turning points (with the so-called resonance tunneling) is
considered. The quantization condition characterizing the asymptotic behavior of resonances is described. Bibliography: 26
titles.
Translated from Problemy Matematicheskogo Analiza, No. 38, December 2008, pp. 93–119. 相似文献
20.
B. A. Aliev 《Differential Equations》2018,54(9):1256-1260
The asymptotic behavior of eigenvalues of a boundary value problem for a secondorder differential-operator equation in a separable Hilbert space on a finite interval is studied for the case in which the same spectral parameter occurs linearly in the equation and quadratically in one of the boundary conditions. We prove that the problem has a sequence of eigenvalues converging to zero. 相似文献