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Displaying similar documents to “Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems”

Breakdown in finite time of solutions to a one-dimensional wave equation.

Mokhtar Kirane, Salim A. Messaoudi (2000)

Revista Matemática Complutense

Similarity:

We consider a special type of a one-dimensional quasilinear wave equation w - phi (w / w) w = 0 in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.

Some results on the well-posedness for systems with time dependent coefficients

Marcello D’Abbicco, Giovanni Taglialatela (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We consider hyperbolic systems with time dependent coefficients and size  2 or  3 . We give some sufficient conditions in order the Cauchy Problem to be well-posed in 𝒞 and in Gevrey spaces.