MR2493876 Seiichiro WAKABAYASHI Seiichiro WAKABAYASHI On the Cauchy problem for Hyperbolic Operators with Nearly Constant Coefficient Principal Part Funkcialaj Ekvacioj. Serio Internacia 51 2008 395--430 http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-3/51_395.pdf http://www.ams.org/mathscinet-getitem?mr=MR2493876 In this paper we shall deal with hyperbolic operators whose principal symbols can be microlocally transformed to symbols depending only on the fiber variables by homogeneous canonical transformations. We call such operators ``hyperbolic operators with nearly constant coefficient principal part.'' Operators with constant coefficient hyperbolic principal part and hyperbolic operators with involutive characteristics belong to this class of operators. We shall give a necessary and sufficient condition for the Cauchy problem to be $C^\infty$ well-posed under some additional assumptions. Namely, we shall generalize ``Levi condition'' and prove that the generalized Levi condition is necessary and sufficient for the Cauchy problem to be $C^\infty$ well-posed. Cauchy problem, Hyperbolic operator, Well-posedness. Primary 35L30; Secondary 35L25. 51-395 2008 On the Cauchy problem for Hyperbolic Operators with Nearly Constant Coefficient Principal Part Seiichiro WAKABAYASHI Seiichiro WAKABAYASHI
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