Regularization of a Boundary Value Problem of an Arbitrary Scalar Wave Diffraction by the Spherical Segment. The Neumann Problem

2006 ◽  
Vol 65 (11) ◽  
pp. 977-994
Author(s):  
Yu. V. Svishchev
Keyword(s):  
Boundary Value Problem ◽  
Neumann Problem ◽  
Wave Diffraction ◽  
Boundary Value ◽  
Spherical Segment ◽  
Scalar Wave ◽  
The Neumann Problem

scholarly journals Pairs of nodal solutions for a Minkowski-curvature boundary value problem in a ball

2019 ◽  
Vol 21 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Alberto Boscaggin ◽  
Maurizio Garrione
Keyword(s):  
Boundary Value Problem ◽  
Neumann Problem ◽  
Boundary Value ◽  
Periodic Problem ◽  
Nodal Solutions ◽  
Shooting Technique ◽  
One Dimensional ◽  
Dimensional Equation

By using a shooting technique, we prove that the quasilinear boundary value problem [Formula: see text] where [Formula: see text] is a ball and [Formula: see text], has more and more pairs of nodal solutions on growing of the parameter [Formula: see text]. The radial Neumann problem and the periodic problem for the corresponding one-dimensional equation are considered, as well.

scholarly journals On the discreteness of the spectra of the Dirichlet and Neumannp-biharmonic problems

2004 ◽  
Vol 2004 (9) ◽  
pp. 777-792 ◽  
Author(s):  
Jiří Benedikt
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Neumann Problem ◽  
Nonlinear Boundary ◽  
Neumann Boundary ◽  
Unbounded Sequence ◽  
The Neumann Problem ◽  
Biharmonic Problems ◽  
Zero Points

We are interested in a nonlinear boundary value problem for(|u″|p−2u″)′​′=λ|u|p−2uin[0,1],p>1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to thenth eigenvalue, has preciselyn−1zero points in(0,1). Eigenvalues of the Neumann problem are nonnegative and isolated,0is an eigenvalue which is not simple, and the positive eigenvalues are simple and they form an increasing unbounded sequence. An eigenfunction, corresponding to thenth positive eigenvalue, has preciselyn+1zero points in(0,1).

SYMMETRY RESULT FOR SOME OVERDETERMINED VALUE PROBLEMS

2008 ◽  
Vol 49 (4) ◽  
pp. 479-494 ◽  
Author(s):  
MOHAMMED BARKATOU ◽  
SAMIRA KHATMI
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problems ◽  
Neumann Problem ◽  
Compatibility Condition ◽  
Mean Curvature ◽  
Boundary Value ◽  
The Maximum Principle ◽  
The Mean ◽  
The Neumann Problem ◽  
Symmetry Result

AbstractThe aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.

A Factorization Method for an Inverse Neumann Problem for Harmonic Vector Fields

2003 ◽  
Vol 10 (3) ◽  
pp. 549-560
Author(s):  
R. Kress
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Neumann Problem ◽  
Vector Fields ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Factorization Method ◽  
Harmonic Vector ◽  
Neumann Boundary Value Problem ◽  
Harmonic Vector Fields

Abstract Extending the previous work on the corresponding inverse Dirichlet problem, we present a factorization method for the solution of an inverse Neumann boundary value problem for harmonic vector fields.

scholarly journals Internal Wave Diffraction by a Strip of an Elastic Plate on the Surface of a Stratified Fluid

2013 ◽  
Vol 18 (1) ◽  
pp. 5-26
Author(s):  
P. Dolai ◽  
D.P. Dolai
Keyword(s):  
Boundary Value Problem ◽  
Small Parameter ◽  
Internal Wave ◽  
Elastic Plate ◽  
Wave Diffraction ◽  
Boundary Value ◽  
Finite Width ◽  
Klein Gordon ◽  
Large Width ◽  
Stratified Liquid

The problem of internal wave diffraction by a strip of an elastic plate of finite width present on the surface of an exponentially stratified liquid is investigated in this paper. Assuming linear theory, the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves a hyperbolic type partial differential equation (PDE), known as the Klein Gordon equation. The method of Wiener-Hopf is utilized in the mathematical analysis to a slightly generalized boundary value problem (BVP) by introducing a small parameter, and the problem is solved approximately for large width of the plate. In the final results, this small parameter is made to tend to zero. The diffracted field is obtained in terms of integrals, which are then evaluated asymptotically in different regions for a large distance from the edges of the plate and the results are interpreted physically.

scholarly journals The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces

2006 ◽  
Vol 13 (2) ◽  
pp. 251-260
Author(s):  
Luis P. Castro ◽  
David Natroshvili
Keyword(s):  
Boundary Value Problem ◽  
Wave Diffraction ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Potential Method ◽  
Wave Number ◽  
Dimensional Case ◽  
Bessel Potential ◽  
Regularity Properties ◽  
Bessel Potential Spaces

Abstract This paper is concerned with a screen type boundary value problem arising from the wave diffraction problem with a reactance condition. We consider the problem in a weak formulation within Bessel potential spaces, and where both cases of a complex and a pure real wave number are analyzed. Using the potential method, the boundary value problem is converted into a system of integral equations. The invertibility of the corresponding matrix pseudodifferential operator is shown in appropriate function spaces which allows the conclusion about the existence and uniqueness of a weak solution to the original problem. Higher regularity properties of solutions are also proved to exist in some scale of Bessel potential spaces, upon the corresponding smoothness improvement of given data. In particular, the 𝐶 α -smoothness of solutions in a neighbourhood of the screen edge is established with arbitrary α < 1 in the two-dimensional case and α < 1/2 in the three-dimensional case.

A BOUNDARY VALUE PROBLEM FOR MONOPOLES OVER A 3-DIMENSIONAL DISK

2004 ◽  
Vol 01 (04) ◽  
pp. 405-422
Author(s):  
ANTONELLA MARINI
Keyword(s):  
Gauge Theory ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Neumann Problem ◽  
Dimensional Reduction ◽  
Boundary Value ◽  
Ginzburg Landau ◽  
Yang Mills ◽  
3 Dimensional ◽  
Well Posed

In this paper we prove the existence of a smooth minimum for the Yang–Mills–Higgs functional over a disk in 3 dimensions among those configurations with monopoles with prescribed degree, which are covariant constant at the boundary. These boundary conditions come essentially from a 4-dimensional generalized Neumann problem for the pure Yang–Mills functional and dimensional reduction. This problem is well-posed only as a gauge theory in dimension 3. It extends analogous results on Ginzburg–Landau vortices in 2 dimensions.

DIFFRACTION BY A SPHEROID

1960 ◽  
Vol 38 (1) ◽  
pp. 128-144 ◽  
Author(s):  
Bertram R. Levy ◽  
Joseph B. Keller
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Expansions ◽  
Series Solution ◽  
Asymptotic Form ◽  
Boundary Value ◽  
Geometrical Theory ◽  
Scalar Wave ◽  
Complex Eigenvalues ◽  
Geometrical Theory Of Diffraction ◽  
Electromagnetic Backscattering

The diffraction of a spherical scalar wave by a hard or soft spheroid is investigated theoretically. First the diffracted field is determined by the geometrical theory of diffraction. Then for comparison the corresponding boundary value problem is solved exactly in terms of a series of products of spheroidal functions. The series involves the "radial" eigenfunctions which correspond to appropriate complex eigenvalues. Asymptotic expansions are derived for these functions for large values of the variable and the parameter. When used in the series solution, these expansions yield the asymptotic form of the diffracted field for incident wavelengths small compared to the spheroid dimensions. This result coincides precisely with that given by the geometrical theory. This agreement provides another verification of that theory. The expression for the field is used to calculate the backscattering and the field on the spheroid. The electromagnetic backscattering is finally computed with the aid of a theorem which relates it to the two scalar results.

scholarly journals About solvability of some boundary value problems for poisson equation in the ball

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 939-946
Author(s):  
Maira Koshanova ◽  
Batirkhan Turmetov ◽  
Kairat Usmanov
Keyword(s):  
Boundary Value Problems ◽  
Neumann Problem ◽  
Poisson Equation ◽  
Fractional Order ◽  
Periodic Boundary ◽  
Differential Operators ◽  
Boundary Value ◽  
Periodic Boundary Value Problems ◽  
Circular Domains ◽  
The Neumann Problem

In the paper we study properties of some integro - differential operators of fractional order. As an application of the properties of these operators for Poisson equation we examine questions on solvability of a fractional analogue of the Neumann problem and analogues of periodic boundary value problems for circular domains. The exact conditions for solvability of these problems are found.

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