Problem of Linear Conjugation with Multipoint Conditions in the Case of Multiple Nodes for Higher-Order Strictly Hyperbolic Homogeneous Equations.

Autor:	Savka, I. Ya., Tymkiv, I. R.
Předmět:	SOBOLEV spaces DIFFERENTIAL equations LEBESGUE measure EQUATIONS CIRCLE INTERPOLATION
Zdroj:	Journal of Mathematical Sciences; Jul2024, Vol. 282 Issue 5, p718-734, 17p
Abstrakt:	We consider the problem in a cylindrical domain of variables t and x , which is the Cartesian product of a segment containing zero and a unit circle and is split into two subdomains by a hyperplane t = 0. In each subdomain, the solution of the problem satisfies the corresponding differential equations with multipoint conditions in the case of multiple nodes and the conditions of linear conjugation on the interface t = 0. The form of the domain imposes additional conditions on the periodicity of the solution with respect to the space variable x. We study the conditions of correct solvability of the problem in the Sobolev space closely related to the problem of small denominators and their estimation. With the help of the metric approach, it is shown that these conditions are satisfied for almost all (with respect to the Lebesgue measure) vectors formed by the interpolation nodes of the multipoint conditions. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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