On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2009
• ISSN: 1812-9471
• Main Authors: Anoshchenko, O., Lysenko, O., Khruslov, E.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106536
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems / O. Anoshchenko, O. Lysenko, E. Khruslov // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 2. — С. 115-122. — Бібліогр.: 6 назв. — англ.

A perturbation of the Poisson equation by a biharmonic operator with a small multiplier ε is considered. The asymptotic behavior of the solution of the Dirichlet problem for this equation as ε → 0 is studied. The gradient of the solution is proved to converge to the gradient of the solution to Poiss...