Before we pursue the analysis of equations and systems with time-dependent coefficients, it is instructive to understand what happens in the case of equations with constant coefficients. One of the very helpful observations available in this case is that after a Fourier transform in the spatial variable
we obtain an ordinary differential equation with constant coefficients which can be solved almost explicitly once we know its characteristics. This works well for frequencies where the characteristics are simple. If they become multiple, the representation breaks down and other methods are required. In the presentation of this part we follow , to which we refer for the detailed arguments and complete proofs of the material in this chapter.
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