Geodesic
A problem with second kind integral conditions for hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1-2 (2016), pp. 33-45

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In this paper, we consider a problem for one-dimensional hyperbolic equation with second kind integral conditions and prove unique solvability. To prove this statement we suggest a new approach. The main idea of it is that given nonlocal integral condition is equivalent with a different condition, nonlocal as well but this new condition enables us to introduce a definition of a generalized solution bazed on an integral identity and derive a priori estimates of a required solution in Sobolev space. This approach shows that integral conditions are closely connected with dynamical conditions.
Keywords: nonlocal problem, integral conditions, hyperbolic equation, generalized solution
Mots-clés : dynamical conditions. 
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     author = {L. S. Pulkina and A. E. Savenkova},
     title = {A problem with second kind integral conditions for hyperbolic equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {33--45},
     publisher = {mathdoc},
     number = {1-2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2016_1-2_a3/}
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L. S. Pulkina; A. E. Savenkova. A problem with second kind integral conditions for hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1-2 (2016), pp. 33-45. http://geodesic.mathdoc.fr/item/VSGU_2016_1-2_a3/