Geodesic
Problem with Steklov conditions for a hyperbolic equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 50-60

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In this paper, we consider a hyperbolic equation with one spatial variable under additional nonlocal conditions and prove the existence of a unique generalized solution. The proof is based on a priori estimates obtained, the Galerkin method, and properties of Sobolev spaces.
Keywords: hyperbolic equation, nonlocal problem, generalized solution, initial-boundary-value problem. 
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     author = {A. V. Dyuzheva},
     title = {Problem with {Steklov} conditions for a hyperbolic equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {50--60},
     publisher = {mathdoc},
     volume = {198},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_198_a4/}
}
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A. V. Dyuzheva. Problem with Steklov conditions for a hyperbolic equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 50-60. http://geodesic.mathdoc.fr/item/INTO_2021_198_a4/