Geodesic
The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 4, pp. 465-482

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We discuss the local existence and uniqueness of solutions of certain nonstrictly hyperbolic systems, with Hölder continuous coefficients with respect to time variable. We reduce the nonstrictly hyperbolic systems to the parabolic ones and by use of the Tanabe-Sobolevski's method and the Banach scale method we construct a semi-group which gives a representation of the solution to the Cauchy problem.

Classification : 35L45, 35A08 
@article{ASNSP_2006_5_5_4_465_0,
     author = {Kajitani, Kunihiko and Yuzawa, Yasuo},
     title = {The {Cauchy} problem for hyperbolic systems with {H\"older} continuous coefficients with respect to the time variable},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {465--482},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
     number = {4},
     year = {2006},
     mrnumber = {2297720},
     zbl = {1170.35474},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_465_0/}
}
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Kajitani, Kunihiko; Yuzawa, Yasuo. The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 4, pp. 465-482. http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_465_0/