A PROBLEM WITH SECOND KIND INTEGRAL CONDITIONS FOR HYPERBOLIC EQUATION

Autor:	L. S. Pulkina, A. E. Savenkova
Rok vydání:	2016
Předmět:	Mathematical analysis Hyperbolic partial differential equation Mathematics
Zdroj:	Vestnik of Samara University. Natural Science Series. 22:33-45
ISSN:	2712-8954 2541-7525
DOI:	10.18287/2541-7525-2016-22-1-2-33-45
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e44d2de6845a529cf0e7296e34a49a0d https://doi.org/10.18287/2541-7525-2016-22-1-2-33-45 Zobrazit plný text záznamu