Geodesic
A problem with the Frankl and Bitsadze--Samarskii condition on the line of degeneracy and on parallel characteristics for a~mixed-type equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2012), pp. 43-52

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In this paper we study a boundary-value problem with the Frankl and Bitsadze–Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation with a singular coefficient. We prove the existence of a solution by the method of integral equations, and we do its uniqueness with the help of the extremum principle.
Keywords: extremum principle, unique solvability, integral equations.
Mots-clés : existence of solution 
@article{IVM_2012_8_a4,
     author = {M. Kh. Ruziev},
     title = {A problem with the {Frankl} and {Bitsadze--Samarskii} condition on the line of degeneracy and on parallel characteristics for a~mixed-type equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {43--52},
     publisher = {mathdoc},
     number = {8},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_8_a4/}
}
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M. Kh. Ruziev. A problem with the Frankl and Bitsadze--Samarskii condition on the line of degeneracy and on parallel characteristics for a~mixed-type equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2012), pp. 43-52. http://geodesic.mathdoc.fr/item/IVM_2012_8_a4/