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Singular hyperbolic systems. VII: Asymptotic analysis for Fuchsian hyperbolic equations in Gevrey classes (2). (English) Zbl 0702.35148
In Part VI [J. Math. Soc. Japan 39, 551-580 (1987; Zbl 0621.35061)] the author defined the irregularity index $$\sigma$$ ($$\geq 1)$$ for a class of Fuchsian hyperbolic operators P and he developed the asymptotic analysis for $$Pu=f$$ in the space of functions of Gevrey classes of exponent s under the assumption $$1<s<\sigma /(\sigma -1)$$. The author investigates the same problem under the assumption $$s=\sigma /(\sigma -1)$$. The typical example is as follows: $P=(t\partial_ t)^ 2- t^{2p}\partial^ 2_ x+a(t,x)t^ q\partial_ x+b(t,x),$ $$\sigma$$ $$=\max \{1,(2p-q)/p\}$$, where p and q are positive integers.
Reviewer: Hidetoshi Tahara

##### MSC:
 35L30 Initial value problems for higher-order hyperbolic equations 35L10 Second-order hyperbolic equations 35C20 Asymptotic expansions of solutions to PDEs