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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2021 Volume 18, Issue 1, Pages 43–53 (Mi semr1345)

This article is cited in 2 papers

Differentical equations, dynamical systems and optimal control

Initial-boundary value problems for degenerate hyperbolic equations

A. I. Kozhanov

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia

Abstract: The aim of the paper is to study solvability in Sobolev spaces initial–boundary value problems for differential equations
$$u_{tt}-\varphi(t)Au+c(x,t)u=f(x,t)$$
in which $A$ is an elliptic operator acting in the spatial variables $x_1$,\ldots,$x_n$ and $\varphi(t)$ is a non-negative function on the segment $[0,T]$. Existence theorems of regular solutions are proven. Some generalizations of the results are also described.

Keywords: hyperbolic equations, degeneration, initial-boundary value problems, regular solutions, existence.

UDC: 517.946

MSC: 35L80, 35L25

Received July 17, 2020, published January 25, 2021

DOI: 10.33048/semi.2021.18.004



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© Steklov Math. Inst. of RAS, 2025