A problem with second kind integral conditions for hyperbolic equation

L. S. Pulkina   ; A. E. Savenkova

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1-2 (2016), pp. 33-45

Résumé

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.

Détail

Keywords: nonlocal problem, integral conditions, hyperbolic equation, generalized solution
Mots-clés : dynamical conditions.

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