Geodesic
Dirichlet problem for Lavrent'ev--Bitsadze equation with loaded summands
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2018), pp. 42-58

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We study the first boundary-value problem for loaded equation of elliptic-hyperbolic type in rectangular domain. We establish a criterion of uniqueness. A solution to the problem is constructed in the form of the sum of a series. In substantiation of existence of a solution to a problem small denominators appear. We obtain the estimates about a separation from zero of denominators with the corresponding asymptotics. They allow to prove existence of a solution in a class of regular solutions.
Keywords: loaded equation of mixed type, Dirichlet's problem, criterion of uniqueness, series, small denominator, estimate
Mots-clés : existence, uniform convergence. 
@article{IVM_2018_9_a4,
     author = {Yu. K. Sabitova},
     title = {Dirichlet problem for {Lavrent'ev--Bitsadze} equation with loaded summands},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {42--58},
     publisher = {mathdoc},
     number = {9},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_9_a4/}
}
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Yu. K. Sabitova. Dirichlet problem for Lavrent'ev--Bitsadze equation with loaded summands. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2018), pp. 42-58. http://geodesic.mathdoc.fr/item/IVM_2018_9_a4/