Cauchy problem for nonstrictly hyperbolic systems in Gevrey classes

Conditions for Well-posedness in Gevrey Classes of the Cauchy Problems for Fuchsian Hyperbolic Operators II

“…The results Independent of the lower order terms were obtained by Ohya [12], Leray-Ohya [8], Steinberg [13], Ivrii [5], Trepreau [15], Bronstein [2], Kajitani [7] and Nishitani [11], which show that the multiplicity of the characteristic roots determines the well-posed class.…”

“…Namely we show that we can determine a function space in which the Cauchy problem for a given Fuchsian hyperbolic operator is well-posed.In the case that the initial surface is non-characteristic, there are many results.The [7] and Nishitani [11], which show that the multiplicity of the characteristic roots determines the well-posed class.On the other hand, it is an interesting problem to study how the lower order terms have an effect on the well-posed class. Ivrii showed the following In [6].…”

“…The [7] and Nishitani [11], which show that the multiplicity of the characteristic roots determines the well-posed class.…”

On a Sufficient Condition for Well-posedness In Gevrey Classes of Some Weakly Hyperbolic Cauchy Problems

“…5 Let # be the number of p(a k , jkY$ in {flA}i^&gn and if we remember (6.4), (6.5) and (5.3), then we obtain that…”

Cauchy problem for hyperbolic systems in Gevrey class. A note on Gevrey indices

“…Kajitani [4], Nishitani [5] and Mizohata [6] developed the study of these problems from another view points.…”