Geodesic
Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 14-24

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We consider a nonlocal boundary-value problem for a third-order parabolic-hyperbolic equation with degeneracy of type and order in the domain of hyperbolicity, containing second-order derivatives in the boundary conditions. Sufficient conditions of the unique solvability of the problem are obtained. The Tricomi method is used to prove the uniqueness theorem for a solution. The solution of the problem is expressed in the explicit form.
Keywords: degenerate hyperbolic equation of the first kind, equation with multiple characteristics, third-order parabolic-hyperbolic equation, mixed boundary-value problem, nonlocal boundary-value problem, Tricomi problem, Tricomi method, Volterra integral equation of the second kind, Fredholm integral equation of the second kind. 
@article{INTO_2018_149_a1,
     author = {Zh. A. Balkizov},
     title = {Nonlocal {Boundary-Value} {Problem} for a {Third-Order} {Equation} of {Parabolic-Hyperbolic} {Type} with {Degeneration} of {Type} and {Order} in the {Hyperbolicity} {Domain}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {14--24},
     publisher = {mathdoc},
     volume = {149},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_149_a1/}
}
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Zh. A. Balkizov. Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 149 (2018), pp. 14-24. http://geodesic.mathdoc.fr/item/INTO_2018_149_a1/