Asymptotic behaviour and stability to linear non-autonomous neutral delay difference equations

This paper is concerned with the asymptotic behaviour and the stability of a class of linear neutral delay difference equations with variable coefficients and constant delays. Via an appropriate solution of the so-called generalized characteristic equation, an asymptotic criterion and a stability result are established.     

Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity

We show that the solution of a semilinear transmission problem between an elastic and a thermoelastic material, decays exponentially to zero. That is, denoting by ?(t) the sum of the first, second and third order energy associated with the system, we show that there exist positive constants C and γsatisfying ?(t) ? C?(0)e^?γt Moreover, the existence of absorbing sets is achieved in the non‐homogeneous case. Copyright © 2002 John Wiley & Sons, Ltd.     

Asymptotic behaviour of the stability parameter for a family of singular-limit Hill's equation

Under some nondegeneracy conditions we give asymptotic formulae for the stability parameter of a family of singular-limit Hill's equation which depends on three parameters. We use the blow-up techniques introduced in [R. Martínez, A. Samà, C. Simó, Analysis of the stability of a family of singular-limit linear periodic systems in R⁴. Applications, J. Differential Equations 226 (2006) 652-686]. The main contribution of this paper concerns the study of the nondegeneracy conditions. We give a geometrical interpretation of them, in terms of heteroclinic orbits for some related systems. In this way one can determine values of the parameters such that the nondegeneracy conditions are satisfied. As a motivation and application we consider the vertical stability of homographic solutions in the three-body problem.     

Asymptotic behaviour of reliability functions

We relate the classes of life distributions based on notions of aging with those that depend on the tail behaviour. This last classification introduces the concepts of outlier-neutral, outlier-prone and outlier-resistant distributions. We prove some results that connect IFR, IFRA, NBU and NBUE definitions with the outlier-resistance concept. Similarly the relationship of DFR, DFRA, NWU and NWUE to outlier-proneness is obtained.     

Asymptotic behaviour of Verblunsky coefficients

Let , ζh≠ζk, h≠k and |ζj|=1, j=1,…,m, and consider the polynomials orthogonal with respect to , , where μ is a finite positive Borel measure on the unit circle with infinite points in its support, such that the reciprocal of its Szeg? function has an analytic extension beyond |z|<1. In this paper we deduce the asymptotic behaviour of their Verblunsky coefficients. By means of this result, an asymptotic representation for these polynomials inside the unit circle is also obtained.     

Asymptotic behaviour of Castelnuovo-Mumford regularity

Let be a polynomial ring over a field. For a graded -module generated in degree at most , the Castelnuovo-Mumford regularity of each of (i) its symmetric power, (ii) its torsion-free symmetric power and (iii) the integral closure of its torsion-free symmetric power is bounded above by a linear function in with leading coefficient at most . For a graded ideal of , the regularity of is given by a linear function of for all sufficiently large . The leading coefficient of this function is identified.

     

Asymptotic behaviour of ground states

We derive the asymptotic behaviour of the ground states of a system of two coupled semilinear Poisson equations with a strongly indefinite variational structure in the critical Sobolev growth case.

     

Asymptotic behaviour of Jain operators

The topic of the present paper are certain approximation operators acting on the space of continous functions on [0,+∞) having polynomial growth. The operators which were defined by Jain in 1972 are based on a probability distribution which is called generalized Poisson distribution. As a main result we derive a complete asymptotic expansion for the sequence of these operators.     

Asymptotic behaviour of disconnection and non-intersection exponents

Summary. We study the asymptotic behaviour of disconnection and non-intersection exponents for planar Brownian motionwhen the number of considered paths tends to infinity. In particular, if η _n (respectively ξ (n, p)) denotes the disconnection exponent for n paths (respectively the non-intersection exponent for n paths versus p paths), then we show that lim _{n →∞} η _n /n = 1 2 and that for a > 0 and b > 0,lim _{n →∞} ξ ([na],[nb])/n = (√ a + √ b) ² /2. Received: 28 February 1996 / In revised form: 3 September 1996     

Asymptotic stability of integral sets

We prove theorems on asymptotic, equiasymptotic, and uniform asymptotic stability of the integral sel of a nonautonomous system of ordinary differential equations.     

Asymptotic behaviour of nonlocal reaction-diffusion equations

The existence of a global attractor in L²(Ω) is established for a reaction-diffusion equation on a bounded domain Ω in R^d with Dirichlet boundary conditions, where the reaction term contains an operator F:L²(Ω)→L²(Ω) which is nonlocal and possibly nonlinear. Existence of weak solutions is established, but uniqueness is not required. Compactness of the multivalued flow is obtained via estimates obtained from limits of Galerkin approximations. In contrast with the usual situation, these limits apply for all and not just for almost all time instants.     

Asymptotic behaviour of high Gaussian minima

We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability of such an event, the extent to which the high level is exceeded, the conditional shape of the process above the high level, and the location of the minimum of the process given that the sample path is above a high level.     

Asymptotic stability of discrete cocycles

We introduce the notion of asymptotic stability of sequences of multifunctions associated with discrete cocycles. Some sufficient conditions for existence of attracting sets are given. The use of the topological (Kuratowski's) limits, as less complicated as commonly used Hausdorff metric, let us to weaken many standard assumptions. We show that in considered case existence of attractor is a property of a cocycle mapping itself and does not depend on properties of a parameter nor a state space. The obtained results generalize earlier on iterated function systems and can be applied for non-autonomous as well as random dynamical systems.     

Asymptotic behaviour of thin poroelastic layers

We consider the deformation behaviour of thin poroelastic layerswhere the governing equations include a non-constant permeability.We consider both the small and long time scale limits and byusing appropriate perturbation series reduce the poroelastic equations to one-dimensional diffusion equations. We particularly consider the cases of an indented porous layer, a layer relaxing after an initial disturbance and a layer with embedded sources.Both axisymmetric and two-dimensional geometries are considered.     

Asymptotic behaviour of nonlinear difference equations

In this paper, we investigate the growth/decay rate of solutions of a class of nonlinear Volterra difference equations. Our results can be applied for the case when the characteristic equation of an associated linear difference equation has complex dominant eigenvalue with higher than one multiplicity. Illustrative examples are given for describing the asymptotic behaviour of solutions in a class of linear difference equations and in several discrete nonlinear population models.