Conditions for the Existence of Solutions of a Periodic Boundary-Value Problem for an Inhomogeneous Linear Hyperbolic Equation of the Second Order. I

Autor:	Yu. A. Mitropol'skii, S. H. Khoma-Mohyl's'ka
Rok vydání:	2005
Předmět:	Exact solutions in general relativity Homogeneous General Mathematics Mathematical analysis Order (group theory) Boundary value problem Algebra over a field Hyperbolic partial differential equation Mathematics
Zdroj:	Ukrainian Mathematical Journal. 57:1077-1088
ISSN:	1573-9376 0041-5995
DOI:	10.1007/s11253-005-0249-9
Popis:	We consider the periodic boundary-value problem u tt − u xx = g(x, t), u(0, t) = u(π, t) = 0, u(x, t + ω) = u(x, t). By representing a solution of this problem in the form u(x, t) = u0(x, t) + ũ(x, t), where u0(x, t) is a solution of the corresponding homogeneous problem and ũ(x, t) is the exact solution of the inhomogeneous equation such that ũ(x, t + ω) u x = ũ(x, t), we obtain conditions for the solvability of the inhomogeneous periodic boundary-value problem for certain values of the period ω. We show that the relation obtained for a solution includes known results established earlier.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a7b3db2d0e94cf8284d3a2d98064f5a6 https://doi.org/10.1007/s11253-005-0249-9 Zobrazit plný text záznamu Plný text ve formátu PDF