One-dimensional models of inviscid, planar liquid sheets surrounded by dynamically passive gases are obtained by means of perturbation methods, integral formulations, series expansions and variational principles. It is shown that integral formulations, series expansions and variational principles provide analogous one-dimensional models under certain approximations for the velocity and pressure...

Article history: Received 25 October 2013 Received in revised form 19 May 2014 Accepted 14 July 2014 Available online 22 July 2014

Although perturbation techniques are widely applied to analyze nonlinear problems in science and engineering, they are however so strongly dependent on small parameters appeared in equations under consideration that they are restricted only to weakly nonlinear problems. For strongly nonlinear problems which don’t contain any small parameters, perturbation techniques are invalid. So, it seems ne...

In this study, we present a direct method to solve nonlinear two-dimensional VolterraHammerestein integral equations in terms of twodimensional piecewise constant block-pulse functions (2D-PCBFs). Properties of these functions and operational matrix of integration together with the product operational matrix are presented and used to transform the integral equation to a matrix equation which co...

‎‎In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...

This study demonstrates that the equations for a two-dimensional steady flow of viscous fluid contain an integral motion, i.e., they have some function whose gradient is zero in solutions hydrodynamic A system partial differential has been derived to calculate this function. It established that, at certain calculation fields reduced solution consisting three first-order with characteristic mani...

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...

A formalism is presented which allows covariant three-dimensional boundstate equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described by these equations with an electromagnetic probe is constructed. This amplitude is shown to be gauge invariant if the formalism is truncated at the same coup...

This work deals with the interaction of P-waves between a moving central crack and a pair of outer cracks situated at the interface of an orthotropic layer and an elastic half-space. Initially, we considered a two-dimensional elastic wave equation in orthotropic medium. The Fourier transform has been applied to convert the basic problem to solve the set of four integral equations. These set of ...