# A mathematical model for Tsunami generation using a conservative velocity-pressure hyperbolic system - Mathematics > Analysis of PDEs

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Abstract: By using the Hugoniot curve in detonics as a Riemann invariant of avelocity-pressure model, we get a conservative hyperbolic system similar to theEuler equations. The only differences are the larger value of the adiabaticconstant = 8.678 instead of 1.4 for gas dynamics and the mass densityreplaced by a strain density depending on the pressure. The model is nothomogeneous since it involves a gravity and a friction term. After the seismicwave reaches up the bottom of the ocean, one gets a pressure wave propagatingtoward the surface, which is made of a frontal shock wave followed by a regulardecreasing profile. Since this regular profile propagates faster than thefrontal shock waves, the amplitude of the pressure wave is strongly reducedwhen reaching the surface. Only in the case of a strong earth tremor theresidual pressure wave is still sufficient to generate a water elevation with asufficient wavelengths enable to propagate as a SaintVenant water wave and tobecome a tsunami when reaching the shore. We describe the construction of themodel and the computation of the wave profile and discuss about the formationor not of a wave.

Author: ** Alain-Yves Le Roux IMB**

Source: https://arxiv.org/