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Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

Boiti, Chiara; Manfrin, Renato — 2001

Serdica Mathematical Journal

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.

A remark on global smooth solutions for quasilinear wave equations

Renato Manfrin — 1994

Rendiconti del Seminario Matematico della Università di Padova

Some results of Gevrey and analytic regularity for semilinear weakly hyperbolic equations of Oleinik type

Renato Manfrin — 1995

Rendiconti del Seminario Matematico della Università di Padova

A note on linear perturbations of oscillatory second order differential equations

Renato Manfrin — 2010

Archivum Mathematicum

Under suitable hypotheses on $γ (t)$ , $λ (t)$ , $q (t)$ we prove some stability results which relate the asymptotic behavior of the solutions of $u^{''} + γ (t) u^{'} + (q (t) + λ (t)) u = 0$ to the asymptotic behavior of the solutions of $u^{''} + q (t) u = 0$ .

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