Geodesic
A Mixed Problem with Integral Condition for the Hyperbolic Equation
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 435-445

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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. 
@article{MZM_2003_74_3_a11,
     author = {L. S. Pulkina},
     title = {A {Mixed} {Problem} with {Integral} {Condition} for the {Hyperbolic} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {435--445},
     publisher = {mathdoc},
     volume = {74},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a11/}
}
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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/