Given a family of discrete shocks φ of a monotone scheme, we prove that the discrete shock profile with rational shock speed η is asymptotically stable with respect to the l1 topology ‖ · ‖1: if u0 − φ ∈ l1, then ‖un − φ·−nη‖1 → 0 as n → ∞ under no restriction conditions of the initial data to the interval [inf φ, supφ]. The asymptotic wave profile is uniquely identified from the above family b...

The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with sample size, the existence and asymptotic normality of the profile likelihood estimator are establis...

We study the temperature profile for a semi-infinite thin layer due to a Gaussian heat source. We follow the time-dependent temperature profile at the center of the top surface of the layer, deriving the asymptotic behavior and both the short time and long time behaviors. We also show that one can estimate thermal properites from various time measurements of the temperature at the center of the...

In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.

Self-focusing of an intense optical beam in a plasma is studied, including the nonlinear effects of both the relativistic electron mass and the ponderomotive potential due to the electromagnetic wave. An exact steady-state asymptotic solution of beam propagation in a localized solitary waveform is obtained in slab geometry. Amplitude-width scaling relations are obtained, which imply that the wi...

In this paper we study the large time behaviour of weak nonnegative solutions of the p-Laplace equation posed in an exterior domain in space dimension N < p with boundary conditions u = 0. The description is done in terms of matched asymptotics: the outer asymptotic profile is a dipole-like self-similar solution with a singularity at x = 0 and anomalous similarity exponents. The inner asymptoti...

A two component system driven by both interface area and interface curvature is studied with a new phase field model. The Euler-Lagrange equation derived from the free energy functional of the system is a fourth order nonlinear partial differential equation. Formal asymptotic analysis shows that if the curvature impact in the system is strong, there exists a bubble profile in each space dimensi...

A cone and a plate rheometer is a laboratory apparatus used to measure the viscosity and other related parameters of a non-Newtonian liquid subject to an applied force. A small drop, of order millimetres, of the liquid is located between the horizontal plate and the shallow cone of the rheometer. Rotation of the cone ensues, the liquid begins to flow and the plate starts to rotate. Liquid param...