RUS  ENG
Полная версия
ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2012, том 3, номер 4, страницы 99–110 (Mi emj107)

Эта публикация цитируется в 6 статьях

The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation

M. S. Salakhitdinov, A. Hasanov

Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

Аннотация: In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R^+_2=\{(x,y)\colon x>0,\ y>0\}$. They contain Kummer's confluent hypergeometric functions in three variables. In this paper, using one of the constructed fundamental solutions, the Dirichlet problem is solved in the domain $\Omega\subset R^+_2$. Using the method of Green's functions, solution of this problem is found in an explicit form.

Ключевые слова и фразы: singular partial differential equation, generalized bi-axially symmetric Helmholtz equation, fundamental solutions, Green's function, Dirichlet problem, Kummer's confluent hypergeometric function in three variables.

MSC: 35A08

Поступила в редакцию: 28.09.2012

Язык публикации: английский



Реферативные базы данных:


© МИАН, 2024