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.
@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://www.numdam.org/item/ASNSP_2006_5_5_4_465_0/}
}
TY - JOUR AU - Kajitani, Kunihiko AU - Yuzawa, Yasuo TI - The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 465 EP - 482 VL - 5 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2006_5_5_4_465_0/ LA - en ID - ASNSP_2006_5_5_4_465_0 ER -
%0 Journal Article %A Kajitani, Kunihiko %A Yuzawa, Yasuo %T The Cauchy problem for hyperbolic systems with Hölder continuous coefficients with respect to the time variable %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 465-482 %V 5 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2006_5_5_4_465_0/ %G en %F ASNSP_2006_5_5_4_465_0
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://www.numdam.org/item/ASNSP_2006_5_5_4_465_0/
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