Abstract
In this chapter we show that the Cauchy problem for symmetric hyperbolic systems is C ∞ well posed for any lower order term proving the existence of solutions and the bound of the supports at the same time, by steering a course somewhat close to the boundary value problems rather than the initial value problems. We give an example, which would be the simplest one, is not symmetrizable but the Cauchy problem is C ∞ well posed for any lower order term. We show the well-posedness by the classical method of characteristic curves. We also give a proof of the Lax-Mizohata theorem exhibiting naive ideas to construct an asymptotic solution to systems which will be used in Chaps. 1 and 2 in a more involved way. The Levi condition for first order systems with characteristics of constant multiplicities is discussed in a somewhat intermediate form. We use this for proving more general result in Chap. 2.
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Nishitani, T. (2014). Introduction. In: Hyperbolic Systems with Analytic Coefficients. Lecture Notes in Mathematics, vol 2097. Springer, Cham. https://doi.org/10.1007/978-3-319-02273-4_1
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DOI: https://doi.org/10.1007/978-3-319-02273-4_1
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