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A PROBLEM WITH SECOND KIND INTEGRAL CONDITIONS FOR HYPERBOLIC EQUATION
- Authors: Pulkina L.S.1, Savenkova A.E.2
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Affiliations:
- Department of Equations of Mathematical Physics, Samara University, 34, Moskovskoye Shosse, Samara, 443086, Russian Federation.
- Department of General Mathematics and Informatics, Samara State Technical University, 244, Molodogvardeyskaya Street, Samara, 443100, Russian Federation.
- Issue: Vol 22, No 1-2 (2016)
- Pages: 33-45
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/4263
- DOI: https://doi.org/10.18287/2541-7525-2016-22-1-2-33-45
- ID: 4263
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Abstract
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.
About the authors
L. S. Pulkina
Department of Equations of Mathematical Physics, Samara University, 34, Moskovskoye Shosse, Samara, 443086, Russian Federation.
Author for correspondence.
Email: morenov.sv@ssau.ru
A. E. Savenkova
Department of General Mathematicsand Informatics, Samara State Technical University, 244, Molodogvardeyskaya Street, Samara, 443100, Russian Federation.
Email: morenov.sv@ssau.ru
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