Homogenization of Electrostatic Problems in Nonlinear Medium with Thin Perfectly Conducting Grids

Автор(и)

  • M.V. Goncharenko Mathematical Division, B. Verkin Institute for Low Temperature Physics & Engineering National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkov, 61103, Ukraine
  • V.I. Prytula Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine 12 Akad. Proscura Str., Kharkov, 61002, Ukraine

Ключові слова:

homogenization, domains with grids, electrostatic, Sobolev - Orlicz spaces.

Анотація

The asymptotic behavior of solutions of the family of nonlinear ellip- tic equations in domains with thin grids concentrating near a hypersurface when measure of the wires tends to zero and the density tends to infinity is investigated. The homogenized equations and the homogenized boundary conditions are derived. The homogenization technique is based on applying of the abstract theorem on homogenization of the nonlinear variational functionals in the Sobolev-Orlicz spaces.

Mathematics Subject Classification: 35B27.

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(1)
Goncharenko, M.; Prytula, V. Homogenization of Electrostatic Problems in Nonlinear Medium with Thin Perfectly Conducting Grids. Журн. мат. фіз. анал. геом. 2006, 2, 424-448.

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