This article is cited in 22 papers

The Dirichlet problem for a loaded mixed-type equation in a rectangular domain

K. B. Sabitov, E. P. Melisheva

Chair of Mathematics and Teaching Principles, Samara State Academy of Social Sciences and Humanities, 26 Antonova-Ovseenko str., Samara, 443090 Russia

Abstract: We establish necessary and sufficient conditions for the unique solvability of the first boundary problem for a loaded equation with the Lavrent'ev–Bitsadze operator in a rectangular domain. We obtain a solution to the stated problem as the sum of the eigenfunction series for the corresponding one-dimensional problem with respect to eigenvalues. We prove the stability of the solution with respect to boundary functions.

Keywords: loaded mixed-type equation, Dirichlet problem, spectral method, uniqueness, existence, stability.

UDC: 517.95

Received: 16.04.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:7, 53–65

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