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We study the homogenization of semilinear elliptic equations in divergence form with discontinuous oscillating coefficients in the whole ℝN. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions u Isin; of boundary value problems when the period ∈ > 0 of the coefficients is small. By extending some of the classical homogenization results for quasi-linear elliptic equations to unbounded domains and, making use of various variational techniques, we shall establish some stability results under Γ-convergence of least energy solutions for such boundary value problems  

The aim of this paper is to approximate the solution of a class of integral equations of the third kind on an unbounded domain. For computing such approximation, the collocation method based on the generalized Laguerre abscissas is considered. In this method, the unknown function is interpolated at the nodal points {ti}i=1 n+1, where {t i } i=1 n are the zeros of generalized Laguerre polynomials and t n+1 =4. Then, the given equation is transformed to the Fredholm integral equation of the second kind. In the sequel, according to the integration interval, we apply the Gauss-Laguerre collocation method on the interval [0,∞) by using the given nodal points. Therefore, the solution of the third... 

In the present study, the fluid characteristics of triangular turbulent jet flow are considered experimentally and numericafly. The results of spatially developed three- dimensional jet, issued from an equilateral triangular nozzle are presented. The jet is discharged to both bounded and unbounded domains. Because of the wind tunnel set up restrictions, the experimental study has done just for the bounded domain. The hot-wire anemometry is used for experimental study. A numerical method employing control volume approach with collocated grid arrangement which couples the velocity and pressure fields with SIMPLEC algorithm is introduced to discrete the governing equations of fluid flow. The... 

The scaled boundary finite element method (SBFEM) is known for its inherent ability to simulate unbounded domains and singular fields, and its flexibility in the meshing procedure. Keeping the analytical form of the field variables along one coordinate intact, it transforms the governing partial differential equations of the problem into a system of one-dimensional (initial–)boundary value problems. However, closed-form solution of the said system is not available for most cases (e.g. transient heat transfer, acoustics, ultrasonics, etc.) since the system cannot be diagonalized in general. This paper aims to establish a numerical tool within the context of the shooting technique to evaluate...