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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.
Under suitable hypotheses on , , we prove some stability results which relate the asymptotic behavior of the solutions of to the asymptotic behavior of the solutions of .
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