Geodesic
About solvability of one problem with nonlocal conditions for hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 4, pp. 36-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article we consider a nonlocal problem with integral condition of the second kind for hyperbolic equation. The choice of a method for investigating problems with nonlocal conditions of the second kind depends on the type of nonintegral terms. In this article we consider the case when the nonintegral term is a trace of required function on the boundary of the domain. To investigate the solvability of the problem we use method of reduction for loaded equation with homogeneous boundary conditions. This method proved to be effective for defining a generalized solution, to obtain apriori estimates and to prove existence of unique generalized solution of the given problem.
Keywords: hyperbolic equation, integral conditions of the II kind, loaded equation.
Mots-clés : nonlocal conditions 
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V. A. Kirichek. About solvability of one problem with nonlocal conditions for hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 4, pp. 36-43. http://geodesic.mathdoc.fr/item/VSGU_2020_26_4_a3/

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