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

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.


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