Geodesic
A Mixed Problem with Integral Condition for the Hyperbolic Equation
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 435-445 
L. S. Pulkina. A Mixed Problem with Integral Condition for the Hyperbolic Equation. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 435-445. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a11/
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     title = {A {Mixed} {Problem} with {Integral} {Condition} for the {Hyperbolic} {Equation}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study a mixed problem for the hyperbolic equation with a boundary Neumann condition and a nonlocal integral condition. We justify the assertion that there exists a unique generalized solution of the problem under consideration. The proof of uniqueness is based on an estimate, derived a priori, in the function space introduced in the paper, while the existence of a generalized solution is proved by the Galerkin method.

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