Geodesic
Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems
Serdica Mathematical Journal, Tome 27 (2001) no. 1, pp. 67-90.

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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.
Keywords: Blow-up, Hyperbolic Systems 
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Boiti, Chiara; Manfrin, Renato. Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems. Serdica Mathematical Journal, Tome 27 (2001) no. 1, pp. 67-90. http://geodesic.mathdoc.fr/item/SMJ2_2001_27_1_a1/