Geodesic
Boundary-Value Problem with Nonlocal Integral Condition for Mixed-Type Equations with Degeneracy on the Transition Line
Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 393-406

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For an elliptic-hyperbolic type equation, the boundary-value problem with nonlocal Samarskii–Ionkin condition in a rectangular domain is solved. Using the spectral analysis method, a uniqueness criterion is established and the existence theorem for the solution of the problem is proved. The solution of the problem is constructed as the sum of a biorthogonal series.
Keywords: elliptic-hyperbolic type equation, boundary-value problem, Samarskii–Ionkin condition, spectral analysis, Bessel's equation, Weierstrass criterion. 
@article{MZM_2015_98_3_a7,
     author = {Yu. K. Sabitova},
     title = {Boundary-Value {Problem} with {Nonlocal} {Integral} {Condition} for {Mixed-Type} {Equations} with {Degeneracy} on the {Transition} {Line}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {393--406},
     publisher = {mathdoc},
     volume = {98},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a7/}
}
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Yu. K. Sabitova. Boundary-Value Problem with Nonlocal Integral Condition for Mixed-Type Equations with Degeneracy on the Transition Line. Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 393-406. http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a7/