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Статья
2013

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


K. B. SabitovK. B. Sabitov, E. P. MelishevaE. P. Melisheva
Русская математика
https://doi.org/10.3103/S1066369X13070062
Abstract / Full Text

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.

Author information
  • Samara State Academy of Social Sciences and Humanities, ul. Antonova-Ovseenko 26, Samara, 443090, RussiaK. B. Sabitov & E. P. Melisheva
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