In the framework solving electromagnetic scattering problems with a Leontovich impedance boundary condition (LIBC), the numerical resolution requires the evaluation of singular integrals appearing in the discretization of the variational formulation. Our main interest is to pricisely evaluate these integrals. Thus, we propose an analytic method to ...
Published in Fluid Dynamics
Abstract—We consider a plane problem on the evolution of perturbations of the surface of an ideal incompressible fluid of finite depth caused by a deep pulsating point source that begins its work in an initially undisturbed medium. The process of establishing surface waves propagating symmetrically in both directions from the source is described. T...
Published in Computational Mathematics and Mathematical Physics
AbstractA singular integral equation of the first kind is considered on the integration interval \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[ - 1,1]$$\end{document...
Published in Russian Mathematics
We study behavior of singular integral at neighborhood of the point at infinity. Its density satisfies the Hölder condition on the any finite part of the real axis, and at the infinity point it vanishes as power of logarithm with exponent lesser than −1.
Published in Journal of Applied and Industrial Mathematics
Under consideration are the issues of numerical solution of a. boundary integral equation describing the vorticity generation process on the streamlined airfoils in meshless vortex methods. The traditional approach based on the quadrature method leads to the necessity of solving a. system of linear algebraic equations with dense matrix. If we consi...
"Harmonic Analysis and Nonlinear Partial Differential Equations". June 25-27, 2018. edited by Hideo Takaoka and Satoshi Masaki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / This is a survey on generalized Campanato spaces with variable growth condition. We first define generalized Campanato spaces...
Published in Mathematical Notes
The paper is devoted to the application of the circle method to the problem of an asymptotics of the weighted number of integer points on multidimensional hyperboloids of a special form. We prove the convergence and positivity of the singular series and obtain an asymptotic formula for the singular integral of this problem. Earlier, only estimates ...
Published in Lobachevskii Journal of Mathematics
We study the behavior of singular integral along the real axis in the neighborhood of the point at infinity, when its density satisfy Hölder condition in any finite part of the real axis and is continuous function in the neighborhood of the point at infinity, which decreases with the order of decreasing same as the lower then the minus first power ...
Published in Fractional Calculus and Applied Analysis
This article discusses several definitions of the fractional Laplace operator L = — (—Δ)α/2 in Rd , also known as the Riesz fractional derivative operator; here α ∈ (0,2) and d ≥ 1. This is a core example of a nonlocal pseudo-differential operator, appearing in various areas of theoretical and applied mathematics. As an operator on Lebesgue spaces ...
Published in Russian Mathematics
We obtain an asymptotic representation of singular integral with the Hilbert kernel near a point, where modulus of continuity of its density behaves itself as inverse value of double logarithm of distance from this point.
