Abstract. Degeneration in a small spatial coordinate of the original initial–boundary-value problem for hyperbolic equations is considered in order to construct more simple models. The problem is investigated in a region whose one space scale is much less than the other scales. This makes it possible to expand the desired functions into power series and hence to reduce the dimension of the problem. However, this comes at the cost of degeneration of the spectrum of the original three-dimensional problem.

Keywords: hyperbolic equations, hyperbolic degeneration, hyperlayer, elastodynamics.