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| 2. |
- Gadyl'shin, R. R., et al.
(författare)
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On the asymptotic behavior of a simple eigenvalue of a boundary value problem in a domain perforated along the boundary
- 2011
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Ingår i: Differential equations. - 0012-2661 .- 1608-3083. ; 47:6, s. 822-831
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Tidskriftsartikel (refereegranskat)abstract
- We consider a boundary value problem for the Laplace operator in a model domain periodically perforated along the boundary. We assume that the homogeneous Neumann condition is posed on the exterior boundary and the homogeneous Dirichlet condition is posed on the boundary of the cavities. We construct and justify the asymptotic expansions of eigenelements of the boundary value problem.
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| 4. |
- Samokhin, Alexander, et al.
(författare)
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Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism
- 2018
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Ingår i: Differential equations. - : Springer Berlin/Heidelberg. - 0012-2661 .- 1608-3083. ; 54:9, s. 1225-1235
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Tidskriftsartikel (refereegranskat)abstract
- Theorems providing the convergence of approximate solutions of linear operator equations to the solution of the original equation are proved. The obtained theorems are used to rigorously mathematically justify the possibility of numerical solution of the 3D singular integral equations of electromagnetism by the Galerkin method and the collocation method.
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| 5. |
- Smirnov, Yu. G., et al.
(författare)
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On the Existence of an Infinite Spectrum of Damped Leaky TE-Polarized Waves in an Open Inhomogeneous Cylindrical Metal–Dielectric Waveguide Coated with a Graphene Layer
- 2023
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Ingår i: Differential equations. - : Springer. - 0012-2661 .- 1608-3083. ; 59:9, s. 1193-1198
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of leaky waves in an inhomogeneous waveguide structure coveredwith a layer of graphene, which is reduced to a boundary value problem for the longitudinalcomponents of the electromagnetic field in Sobolev spaces. A variational statement of the problemis used to determine the solution. The variational problem is reduced to the study of an operatorfunction. The properties of the operator function necessary for the analysis of its spectralproperties are investigated. Theorems on the discreteness of the spectrum and on the distributionof the characteristic numbers of the operator function on the complex plane are proved.
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