## 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.

### MSC:

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

### Keywords:

regular solutions; existence
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