Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients (Case: H0 > 0)

Autor:	Hovik A. Matevossian, Maria V. Korovina, Vladimir A. Vestyak
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	asymptotic behavior of solutions second-order hyperbolic equation periodic coefficients Cauchy problem Hill operator Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 16, p 2963 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10162963
Popis:	The main goal of this article is to study the behavior of solutions of non-stationary problems at large timescales, namely, to obtain an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients at large values of the time parameter t. To obtain an asymptotic expansion as t→∞, the basic methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of the Hill operator with periodic coefficients in the case when the operator is positive: H0>0.
Databáze:	Directory of Open Access Journals
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