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Kozhanov, A. I.

Initial-boundary value problems for degenerate hyperbolic equations. (Russian. English summary) Zbl 1458.35276

Sib. Èlektron. Mat. Izv. 18, No. 1, 43-53 (2021).
Summary: 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 \(x_1,\dots, x_n\) 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.

Cited in 1 Document

MSC:

35L80 Degenerate hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations

Keywords:

regular solutions; existence
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\textit{A. I. Kozhanov}, Sib. Èlektron. Mat. Izv. 18, No. 1, 43--53 (2021; Zbl 1458.35276)
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References:

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