Geodesic
The Dirichlet problem for a~loaded mixed-type equation in a~rectangular domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 62-76

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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, stability.
Mots-clés : existence 
@article{IVM_2013_7_a5,
     author = {K. B. Sabitov and E. P. Melisheva},
     title = {The {Dirichlet} problem for a~loaded mixed-type equation in a~rectangular domain},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--76},
     publisher = {mathdoc},
     number = {7},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_7_a5/}
}
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K. B. Sabitov; E. P. Melisheva. The Dirichlet problem for a~loaded mixed-type equation in a~rectangular domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 62-76. http://geodesic.mathdoc.fr/item/IVM_2013_7_a5/