Open AccessON A CERTAIN PROBLEM FOR A WAVE EQUATION
Author(s) -
Сергей Александрович Бейлин
Publication year - 2011
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2011-17-5-12-17
Subject(s) - mathematics , sobolev space , generalization , hyperbolic partial differential equation , mathematical analysis , wave equation , string (physics) , boundary (topology) , boundary value problem , space (punctuation) , oscillation (cell signaling) , partial differential equation , mathematical physics , computer science , biology , genetics , operating system
In this paper a hyperbolic equation with non-classical boundary conditionsfor a hyperbolic equation is studied. This problem can be viewed as the generalization of the problem about the oscillation of the string if it ends experiencethe resistance of medium. The unique solvability of the problem is proved. Theprove of solvability is based on the received a priory estimates in Sobolev space.