This paper is devoted to the study of the extention of the existence time of solutions in Sobolev spaces to the Cauchy problem for Kirchhoff equations.
Kunihiko KAJITANI. Atsushi SATOH. "On extension of solutions of Kirchhoff equations." J. Math. Soc. Japan 56 (2) 405 - 416, April, 2004. https://doi.org/10.2969/jmsj/1191418637