Geodesic
Problem with shift on parallel characteristics for Gellerstedt equation with singular coefficient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 61-70

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We study correctness for a problem with an analog of Frankl condition on a degeneration line segment and dislocation conditions on parallel characteristics for a singular coefficient Gellerstedt equation. With the help of maximum principle we prove uniqueness of a solution to the problem and with the method of integral equations we prove the existence of a solution to the problem.
Keywords: shift condition, parallel characteristics, analog of Frankl condition, isolated singularities of first order, Wiener–Hopf equation, index. 
@article{IVM_2017_5_a6,
     author = {M. Mirsaburov and S. T. Chorieva},
     title = {Problem with shift on parallel characteristics for {Gellerstedt} equation with singular coefficient},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {61--70},
     publisher = {mathdoc},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_5_a6/}
}
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M. Mirsaburov; S. T. Chorieva. Problem with shift on parallel characteristics for Gellerstedt equation with singular coefficient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 61-70. http://geodesic.mathdoc.fr/item/IVM_2017_5_a6/