Homogenization of Maxwell's Equations in Domains with Dense Perfectly Conducting Grids

We consider Maxwell’s equations in domains that are complements to connected, grid-like sets formed by intersecting thin wires. We impose the boundary conditions that correspond to perfectly conducting wires, and study the asymptotic behavior of solutions as grids are becoming thinner and denser. We derive a homogenized system of equations describing the leading term of the asymptotics. Assuming that a Korn-type inequality holds, we validate the homogenization procedure

Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain

We consider a boundary-value problem for the Poisson equation in a strongly perforated domain Ωε = Ω\Fε ⊂ Rⁿ (n ≥ 2) with non-linear Robin's condition on the boundary of the perforating set Fε. The domain Ωε depends on the small parameter ε > 0 such that the set Fε becomes more and more loosened and distributes more densely in the domain Ω as ε→0. We study the asymptotic behavior of the solution uε(x) of the problem as ε→0. A homogenized equation for the main term u(x) of the asymptotics of uε(x) is constructed and the integral conditions for the convergence of uε(x) to u(x) are formulated

How to superize Liouville equation

So far, there are described in the literature two ways to superize the Liouville equation: for a scalar field (for $N\leq 4$) and for a vector-valued field (analogs of the Leznov--Saveliev equations) for N=1. Both superizations are performed with the help of Neveu--Schwarz superalgebra. We consider another version of these superLiouville equations based on the Ramond superalgebra, their explicit solutions are given by Ivanov--Krivonos' scheme. Open problems are offered

Splitting of some nonlocalized solutions of the Korteweg-de Vries equation into solitons

SIGLEAvailable from TIB Hannover: RR 5549(287)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman