In this section, I summarize the main results of the theory of first order evolutionary partial differential equation systems. I do this by first developing the theory of linear constant coefficients evolution equation systems in , that is, equations of the type:
What follows is a short account of Chapter II of , see also Chapter IV of . After this, I indicate what aspects of the theory generalize to quasi-linear systems, and under which further assumptions this is so. I also give some indications of the relation of this theory to the stability issues of numerical simulations. This section can be skipped by those not interested in the mathematical theory itself or those who already know it.
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