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| I will talk about quasilinear first order systems, and specifically on the onset of instabilities for a hyperbolic to non hyperbolic transition. My work is based on the method developed by Guy M\' etivier in 2005, which proves the existence of a family of analytical solutions that grow exponentially in time. This proves the Hadamard instability of the system: even a small perturbation of an initial datum lead to a solution infinitely distant to the reference solution in a very short time. |
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