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Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients

100%
Melnikov Y.
Open Mathematics
|
2010
|
tom 8
|
nr 1
53-72
EN
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable for equations with piecewise-constant coefficients.
2
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Analyzing nonlocal effects in the plasmon spectra of a metal slab by the Green’s function technique for hydrodynamic model

100%
Kang N., Miškovic Z. L., Zhang Y.-Y., Song Y.-H., Wang Y.-N.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2014
|
tom 3
|
nr 1
EN
We study the dynamic response of a metal slab containing electron gas described by the hydrodynamic model with dispersion. The resulting wave equation for the perturbed electron density is solved by means of the Green’s function that satisfies Neumann boundary conditions at the endpoints of the slab. This solution is coupled with the electrostatic potential, which is expressed in terms of the Green’s function for the Poisson equation for a layered structure consisting of three dielectric regions. As an illustration, a set of dispersion relations for eigenfrequencies is deduced for the plasma oscillations in the electron gas, corresponding to both the surface and the bulk modes of even and odd symmetry with respect to the center of the metal slab.
3
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Total curvature and volume of foliations on the sphere S 2

88%
Fawaz A.
Open Mathematics
|
2009
|
tom 7
|
nr 4
660-669
EN
In this paper we study a curvature integral associated with a pair of orthogonal foliations on the Riemann sphere S 2 and we compute the minimal value of the volume of meromorphic foliations.
4
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Positivity conditions and bounds for Green’s functions for higher order two-point BVP

88%
Gil’ M.
Open Mathematics
|
2011
|
tom 9
|
nr 5
1156-1163
EN
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear equations are also discussed.
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