Kreiss Symmetrizers for Hyperbolic-Parabolic Systems

This chapter is entirely devoted to the proof of Theorem 7.5.2. For strictly hyperbolic equations the construction of symmetrizers is due to O. Kreiss ([Kre] augmented with J. Ralston’s note [Ral], see also [Ch-Pi]). It was then noticed by A. Majda and S. Osher ([Ma-Os], [Maj]) that the strict hyperbolicity can be somewhat relaxed and that the construction extends to systems satisfying a block structure condition. Finally, it is proven in [Mé3] that the block structure condition is satisfied for all hyperbolic systems with constant multiplicity. We discuss in this chapter the extension of Kreiss construction to hyperbolic-parabolic systems given in [MZ1].