The purpose of this article is to study the persistence of solution of a hyperbolic system under small viscous perturbation. Here, the solution of the hyperbolic system is supposed to be periodic: it is a periodic perturbation of a roll-wave. So, it has an infinity of shocks. The proof of the persistence is based on an expansion of the viscous solution and estimates on Green’s functions. Keywor...

We develop an approximate analytical solution for the shape of a nonaxisymmetric sessile drop using regular perturbation methods and ignoring gravity. We assume that the pinned, contorted triple-line shape is known and is a small perturbation of the circular footprint of a spherical cap. We obtain an analytical solution using regular perturbation methods that we validate by comparing to the num...

The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the correspondig solution of the Bernoulli-Euler beam.The problem of convergence is related to a Singular Perturbation Problem. The main tool in solving this problem is a weak version of a lower bound for hyperbolic polynomials.

In this paper, we present homotopy perturbation method (HPM) for solving the Korteweg-de Vries (KdV) equation and convergence study of homotopy perturbation method for nonlinear partial differential equation. We compared our solution with the exact solution and homotopy analysis method (HAM). The results show that the HPM is an appropriate method for solving nonlinear equation.

The dynamics is investigated on the delayed regulation model under period-2 perturbation described as x(t+ 1) = {A + (−1)te}x(t){1 − x(t − 1)}, t = 1, 2, 3 . . . The edependences of the bifurcation points are analyzed through usual stability analysis of fixed point and periodic solution, however one of them is derived through the stability analysis of the “virtual” period-2 solution. key words:...

In this paper, the homotopy perturbation method and a modified homotopy perturbation method are used for analytical treatment of the wave equation and some nonlinear diffusion equations, respectively. Some examples are given to illustrate that a suitable choice of an initial solution can lead to the exact solution, this revealing the reliability and effectiveness of the method. © 2009 Elsevier ...

This paper studies the non-spherical perturbations of the continuously selfsimilar critical solution of the gravitational collapse of a massless scalar field (the Roberts solution). The exact analysis of the perturbation equations reveals that there are no growing non-spherical perturbation modes. PACS numbers: 04.70.Bw, 05.70.Jk Typeset using REVTEX ∗Email: [email protected]