ON THE BLOW-UP OF THE SOLUTIONS OF A QUASI-LINEAR WAVE-EQUATION WITH A SEMILINEAR SOURCE-TERM

Authors
DIAS JP FIGUEIRA M
Citation
Jp. Dias et M. Figueira, ON THE BLOW-UP OF THE SOLUTIONS OF A QUASI-LINEAR WAVE-EQUATION WITH A SEMILINEAR SOURCE-TERM, Mathematical methods in the applied sciences, 19(14), 1996, pp. 1135-1140
Citations number
6
Categorie Soggetti
Mathematical Method, Physical Science",Mathematics
Journal title
Mathematical methods in the applied sciences → ACNP
ISSN journal
01704214
Volume
19
Issue
14
Year of publication
1996
Pages
1135 - 1140
Database
ISI
SICI code
0170-4214(1996)19:14<1135:OTBOTS>2.0.ZU;2-Y
Abstract
In this paper, following the ideas of Lax, we prove a blow-up result f or a class of solutions of the equation phi(tt) - phi(xx) - phi(x)(2) phi(xx) - phi(3) = 0, corresponding, in certain cases, to the developm ent of a singularity in the second derivatives of phi. These solutions solve locally (in time) the Cauchy problem for smooth initial data be longing to the uniformly local Sobolev spaces considered by Kato and b y Majda.