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
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.