Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 27, No 1, (2001), 67p-90p
We present some results on the formation of singularities
for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut +
A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions
(weaker than genuine non-linearity), we prove that the first order derivative
of the solution blows-up in finite time.