On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems

Автор(и)

  • O. Anoshchenko Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University 4 Svobody Sq., Kharkiv, 61077, Ukraine
  • O. Lysenko Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University 4 Svobody Sq., Kharkiv, 61077, Ukraine
  • E. Khruslov Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkiv, 61103, Ukraine

Ключові слова:

singular perturbation, elliptical equations, the Green functions.

Анотація

A perturbation of the Poisson equation by a biharmonic operator with a small multiplier e is considered. The asymptotic behavior of the solution of the Dirichlet problem for this equation as e → 0 is studied. The gradient of the solution is proved to converge to the gradient of the solution to Poisson equation in L1 (W) as e → 0. The difference of the gradients is also estimated.

Mathematics Subject Classification: 35B25, 35J05, 35J75, 35J40.

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Опубліковано

2009-04-29

Як цитувати

(1)
Anoshchenko, O.; Lysenko, O.; Khruslov, E. On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems. J. Math. Phys. Anal. Geom. 2009, 5, 115-122.

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