The Asymptotic Behaviour of the Solutions of a Degenerate Reaction-diffusion Problem

Consider in this paper the existence, uniqueness and asymptotic behaviour of the solutions of the mixed problem for a class of degenerate quasilincar parabolic equations and properties of the corresponding stationary solutions.     

The Asymptotic Behaviour of a Stochastic 3D LANS-α Model

The long-time behaviour of a stochastic 3D LANS-α model on a bounded domain is analysed. First, we reformulate the model as an abstract problem. Next, we establish sufficient conditions ensuring the existence of stationary (steady state) solutions of this abstract nonlinear stochastic evolution equation, and study the stability properties of the model. Finally, we analyse the effects produced by stochastic perturbations in the deterministic version of the system (persistence of exponential stability as well as possible stabilisation effects produced by the noise). The general results are applied to our stochastic LANS-α system throughout the paper.     

一类界面化学反应模型的解的渐近性

本文建立了一个界面化学反应模型,这个模型是一个具有非线性边界条件的抛物型反应扩散方程组．通过建立并求解关于方程组的解的微分不等式,我们得到了解及其任意阶导数在Ｌ∞的收敛速率估计．     

The Axisymmetric Laminar Plume: Asymptotic Solution for Large Prandtl Number

The shapes of a steadily translating pair of equal and opposite vortices with vortex sheets on their boundaries is determined. A continuum of solutions is found to exist between the two extremes: a hollow vortex pair and a vortex pair with no vortex sheets.     

Asymptotic Behaviour of Convolution Semigroups

In this paper, necessary and sufficient conditions are given for U * μ^*n to converge uniformly on the real axis; here $\mu$ is a nonsingular probability measure on ℝ, and U is a Banach space valued L^∞-function. A connection to uniform convergence of Cesaro mean values is shown. By applying the results to extended orbits of bounded C_0-semigroups on a Banach space X one can relate both kernel and range of the respective generator with those of the derivative operator on L^∞(X). Ergodic theorems and consequences for subordinated semigroups, in particular for holomorphic semigroups, are deduced.     

Asymptotic Behavior of Micropolar Fluid Flow Through a Curved Pipe

We study the stationary motion of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. An asymptotic solution is found, showing explicitly the effects of pipe’s distortion and microstructure on the effective behavior of the flow. We justify the obtained model by proving the corresponding error estimate.     

The Asymptotic Behaviour and Blow-up Properties of Solutions of a Non-local Burgers' Equation

In this paper, we continue the work of [1] and obtain a complete picture of asymptotic behavior and blow-up properties of solutions of a non-local Burgers' equation.     

Asymptotic Behaviour of the Castelnuovo-Mumford Regularity

In this paper the asymptotic behavior of the Castelnuovo$ndash;Mumford regularity of powers of a homogeneous ideal I is studied. It is shown that there is a linear bound for the regularity of the powers I whose slope is the maximum degree of a homogeneous generator of I, and that the regularity of I is a linear function for large n. Similar results hold for the integral closures of the powers of I. On the other hand we give examples of ideal for which the regularity of the saturated powers is asymptotically not a linear function, not even a linear function with periodic coefficients.     

Asymptotic Behaviour of a Random Walk Killed on a Finite Set

We study asymptotic behavior, for large time n, of the transition probability of a two-dimensional random walk killed when entering into a non-empty finite subset A. We show that it behaves like \(4 \tilde u_{A}(x) \tilde u_{-A}(-y) (\lg n)^{-2} p^{n}(y- x)\) for large n, uniformly in the parabolic regime \(|x|\vee |y| =O(\sqrt n)\), where p ⁿ (y-x) is the transition kernel of the random walk (without killing) and \(\tilde u_{A}\) is the unique harmonic function in the ‘exterior of A’ satisfying the boundary condition \(\tilde u_{A}(x) \sim \lg |x|\) at infinity.     

The Asymptotic Behavior of the Ruin Probability within a Random Horizon

Subject to the assumption that the common distribution of claim sizes belongs to the extendedregular variation class,the present work obtains a simple asymptotic formula for the ruin probability within arandom or nonrandom horizon in the renewal model.     

On the Asymptotic Geometry of Nonpositively Curved Manifolds

In this paper we derive new asymptotic properties of all Hadamard manifolds admitting compact quotients. We study the growth function of the volume of geodesic spheres, generalizing the work of Margulis in the case of negative curvature. We show that the growth is of purely exponential type if and only if the Hadamard manifold is of rank 1. In general, there is a polynomial deviation from purely exponential behavior, depending in an unexpected way on the rank of the manifold. Furthermore, we obtain new results on the growth rate of closed geodesics on compact rank 1 spaces. Submitted: August 1996, final version: April 1997     

On the Asymptotic Behaviour of a Certain Non-linear Difference Equation

Arising from the study of the convergence properties of a rationalapproximation method for determining a zero of the functionf(x)is a certain non-linear difference equation. This equation hasthe form v_n+1 = g_p–1(v_n)/g_p(v_n), Where g_p(v_n) is a polynomialin v_n whose coefficients depend on a parameter p, the orderof the zero of f The asymptotic behaviour of the differenceequation is studied and it is shown that if there is a limitorder of convergence it is always linear for multiple zeros.     

Boundedness and Asymptotic Behaviour of Solutions of a Second-Order Nonlinear System

Consider the second-order nonlinear system where a is a positive and continuous function onR:(– , ), b, c and h are continuous functions on R, ande is a continuous function on I:[0, ). We obtain a sufficientcondition for all solutions of (*) to be bounded, and obtaina sufficient condition for all solutions of (*) to tend to zero.Our results can be applied to the well-known equation which substantially improves and extendsseveral known results in the literature.     

一类三阶有理差分方程的奇点集和解的渐近性

研究三阶有理差分方程x_(n+1)=ax_(n-1)+x_(n-1)x_n/bx_(n-2)+cx_n,n=0,1,2,...的奇点集和解{x_n}_(n=-2)~∞的渐近性,其中a,b,c∈R,初始值x_(-2),x_(-1),x_0∈R.由a,b,c的取值的不同,而得到解的不同的渐近性.     

Asymptotic Problems of Reconstructing a High-Frequency Source of a Wave Equation

Mathematical Notes -     

Asymptotic Solution of the Problem on an Accelerated Source of High-Frequency Oscillations

The problem of the wave field of a source moving in an inhomogeneous medium is considered. It is assumed that the velocity of the source is less than the velocity of sound for t < 0 and is greater than this velocity for t > 0 (subsonicsupersonic transition). An asymptotic expansion for the wave field in a neighborhood of the source is constructed on the basis of the well-known Hadamard ansatz. The expansion derived is uniform with respect to the velocity of the source and contains new special functions. These functions are generalizations of the Hankel and Bessel functions and possess some remarkable properties. Bibliography: 7 titles.     

三维Wigner-Poisson方程解的渐近性

考虑三维ＷＰ方程的Ｃａｕｃｈｙ问题,在吸引力场的情形下,证明了解的拟渐近性．