Geodesic
Solvability of a nonlocal problem with integral conditions of the II kind for one-dimensional hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 4, pp. 22-28

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In this paper we consider a nonlocal problem with integral conditions of the II kind for one-dimensional hyperbolic equation. Nonlocal conditions of the second kind differ in type of non-integral terms, that may contain traces of required solution and traces of derivatives. This difference turns out to be significant for choosing a method for investigating the solvability of the problem. In this work we consider the case when nonintegral terms are traces of required solution on boundary of the domain. To investigate the solvability of the problem we use method of reduction to the boundary problem for loaded equation. This method allowed us to define a generalized solution, to obtaim apriori estimates and to prove existence of unique generalized solution of the given problem.
Keywords: hyperbolic equation, nonlocal problem, integral condition of the II kind, loaded equation, generalized solution. 
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     author = {V. A. Kirichek},
     title = {Solvability of a nonlocal problem with integral conditions of the {II} kind for one-dimensional hyperbolic equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {22--28},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2019_25_4_a2/}
}
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V. A. Kirichek. Solvability of a nonlocal problem with integral conditions of the II kind for one-dimensional hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 4, pp. 22-28. http://geodesic.mathdoc.fr/item/VSGU_2019_25_4_a2/