Jp. Dias et M. Figueira, EXISTENCE OF A WEAK SOLUTION FOR A QUASI- LINEAR WAVE-EQUATION WITH ASEMILINEAR SOURCE-TERM, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 322(7), 1996, pp. 619-624
We prove in this Note, by applying the compensated compactness method,
following the ideas of Tartar [5] and DiPerna [1], the existence, in
R x [0, +infinity[, of a weak solution for the Cauchy problem for the
quasilinear equation phi(tt)-phi(xx)-phi(x)(2) phi(xx)+phi(3)=0.