On Asymptotic Properties of Maximal Tubes and Bands in a Neighborhood of an Isolated Singularity in Minkowski Space

We study the asymptotic behavior of maximal surfaces like bands and tubes in a neighborhood of an isolated singular point. In particular, we prove possibility of expansion of the radius vector of a two-dimensional surface in a power series with real-analytic coefficients in the time coordinate. We show also that the tangent rays at a singular point constitute a light-like surface. We prove an exact estimate for the existence time for multidimensional maximal tubes in terms of their asymptotic behavior at a singular point and describe completely the class of surfaces on which this estimate is attained.     

On Asymptotic Properties of Maximal Tubes and Bands in a Neighborhood of an Isolated Singularity in Minkowski Space

We study the asymptotic behavior of maximal surfaces like bands and tubes in a neighborhood of an isolated singular point. In particular, we prove possibility of expansion of the radius vector of a two-dimensional surface in a power series with real-analytic coefficients in the time coordinate. We show also that the tangent rays at a singular point constitute a light-like surface. We prove an exact estimate for the existence time for multidimensional maximal tubes in terms of their asymptotic behavior at a singular point and describe completely the class of surfaces on which this estimate is attained.     

Asymptotic behavior of Bayes estimators for hidden Markov models with application to ion channels

In this paper we study the asymptotic behavior of Bayes estimators for hidden Markov models as the number of observations goes to infinity. The theorem that we prove is similar to the Bernstein—von Mises theorem on the asymptotic behavior of the posterior distribution for the case of independent observations. We show that our theorem is applicable to a wide class of hidden Markov models. We also discuss the implication of the theorem’s assumptions for several models that are used in practical applications such as ion channel kinetics.      

Asymptotic Representations for Solutions of One Class of Systems of Quasilinear Differential Equations

We establish asymptotic representations for solutions of one class of systems of differential equations appearing in the investigation of the asymptotic behavior of nth-order quasilinear differential equations.     

The Markov chain asymptotics of random mapping graphs

In this paper the limit behavior of random mappings with n vertices is investigated. We first compute the asymptotic probability that a fixed class of finite non-intersected subsets of vertices are located in different components and use this result to construct a scheme of allocating particles with a related Markov chain. We then prove that the limit behavior of random mappings is actually embedded in such a scheme in a certain way. As an application, we shall give the asymptotic moments of the size of the largest component.     

Exponential Attractor for a Class of Nonclassical Diusion Equation

In this paper, we consider the asymptotic behavior of solutions for a class of nonclassical diffusion equation. We show the squeezing property and the existence of exponential attractor for this equation. We also make the estimates on its fractal dimension and exponential attraction.     

Asymptotic behavior of the spectrum of combination scattering at Stokes phonons

For a class of polynomial quantum Hamiltonians used in models of combination scattering in quantum optics, we obtain the asymptotic behavior of the spectrum for large occupation numbers in the secondary quantization representation. Hamiltonians of this class can be diagonalized using a special system of polynomials determined by recurrence relations with coefficients depending on a parameter (occupation number). For this system of polynomials, we determine the asymptotic behavior a discrete measure with respect to which they are orthogonal. The obtained limit measures are interpreted as equilibrium measures in extremum problems for a logarithmic potential in an external field and with constraints on the measure. We illustrate the general case with an exactly solvable example where the Hamiltonian can be diagonalized by the canonical Bogoliubov transformation and the special orthogonal polynomials degenerate into the Krawtchouk classical discrete polynomials.     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.     

W2,2 interior convergence for some class of elliptic anisotropic singular perturbations problems

In this paper, we deal with anisotropic singular perturbations of some class of elliptic problems. We study the asymptotic behavior of the solution in a certain second-order pseudo Sobolev space.     

Asymptotic behavior and stability of second order neutral delay differential equations

We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed point method is introduced as a third approach to study the asymptotic behavior. We conclude the paper with an application to a mechanical model of turning processes.     

Asymptotic behavior of nonlinear difference systems

In this paper, we consider two-dimensional nonlinear difference systems of the form

We classify their solutions according to asymptotic behavior and give some necessary and sufficient conditions for the existence of solutions of such classes.     

Positive Solutions to Second Order Singular Differential Equations Involving the One-Dimensional M-Laplace Operator

We consider a class of second order quasilinear differential equations with singular ninlinearities. Our main purpose is to investigate in detail the asymptotic behavior of their solutions defined on a positive half-line. The set of all possible positive solutions is classified into five types according to their asymptotic behavior near infinity, and sharp conditions are established for the existence of solutions belonging to each of the classified types.     

Turnpike theorem for a class of set-valued mappings

In this work we study the asymptotic behavior of optimal trajectories for a class of superlinear mappings arising in economic dynamics. We establish the existence of an open everywhere dense subset F of the space of set-valued mappings such that each mapping fron F has the turnpike property.     

On the method of images and the asymptotic behavior of first-passage times

This paper studies the large-t behavior of the boundary generated by the method of images for the first-passage-time problem. We show that this behavior is characterized by certain properties of the Laplace transform of the input measure. Such properties also determine the asymptotic behavior of the first-passage-time density. Most of the paper assumes a positive input measure, which generates a concave boundary. The last section, however, discusses a non-positive measure. We obtain a sufficient condition for the boundary to be convex.     

Large solutions for quasilinear elliptic equation with nonlinear gradient term

We study the existence, asymptotic behavior near the boundary and uniqueness of large solutions for a class of quasilinear elliptic equation with a nonlinear gradient term. By constructing the suitable blow-up upper and lower solutions, we obtain the existence and the asymptotic behavior of radial large solutions of the problem in balls and then derive the existence of solutions in a general domain by a comparison argument. By using a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of any nonnegative solution of it near the boundary. The uniqueness is shown by a standard argument.     

On the asymptotic behavior of solutions of nonlinear second-order parabolic equations

We study the asymptotic behavior as t → +∞ of solutions to a semilinear second-order parabolic equation in a cylindrical domain bounded in the spatial variable. We find the leading term of the asymptotic expansion of a solution as t → +∞ and show that each solution of the problem under consideration is asymptotically equivalent to a solution of some nonlinear ordinary differential equation.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

一类拟抛物粘性扩散方程的整体吸引子

本文考虑出现在人口动力学及稳定分层粘性湍动慢剪切流的热与质量传输理论中一类拟抛物粘性扩散方程解的渐近性态．证明了有限维整体吸引子的存在性．     

Global Dispersive Solutions for the Gross–Pitaevskii Equation in Two and Three Dimensions

We study asymptotic behaviour at time infinity of solutions close to the non-zero constant equilibrium for the Gross–Pitaevskii equation in two and three spatial dimensions. We construct a class of global solutions with prescribed dispersive asymptotic behavior, which is given in terms of the linearized evolution. Submitted: May 24, 2006. Revised: December 21, 2006. Accepted: February 6, 2007.     

Transition densities of spectrally positive Lévy processes

Lithuanian Mathematical Journal - We deduce the asymptotic behavior of transition densities for a large class of spectrally one-sided Lévy processes of unbounded variation satisfying mild...