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 B. Verkin Institute for Low Temperature Physics and Engineering of the 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 $\varepsilon$ is considered. The asymptotic behavior of the solution of the Dirichlet problem for this equation as $\varepsilon\to 0$ is studied. The gradient of the solution is proved to converge to the gradient of the solution to Poisson equation in $L_1(\Omega)$ as $\varepsilon\to 0$. The difference of the gradients is also estimated.

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

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Як цитувати

(1)
Anoshchenko, O.; Lysenko, O.; Khruslov, E. On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems. Журн. мат. фіз. анал. геом. 2009, 5, 115-122.

Номер

Том 5 № 2 (2009)

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