This article is cited in 7 papers

Mathematics

Dirichlet problem for loaded equation of Lavrentiev–Bizadze

E. P. Melisheva

Dept. of Mathematical Analysis, Samara State Academy of Social Sciences and Humanities, Samara, 443090, Russian Federation

Abstract: Necessary and sufficient conditions of the uniqueness of solution of the first boundary problem for the loaded equtation of Lavrentiev–Bitsadze in the rectangular area are established in this work.The solution of the task in view is constructed in the form of the number sum on the own functions of a corresponding one-dimensional problem on the own values.

Keywords: loaded equation of the mixed type, Dirichlet problem, spectral method, uniqueness, existence.

UDC: 517.95

Received: 12.05.2010
Revised: 12.05.2010