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Compacité par compensation pour une classe de systèmes hyperboliques de p ≥ 3 lois de conservation.

Sylvie Benzoni-Gavage;  Denis Serre — 1994

Revista Matemática Iberoamericana

We are concerned with a strictly hyperbolic system of conservation laws u + f(u) = 0, where u runs in a region Ω of R, such that two of the characteristic fields are genuinely non-linear whereas the other ones are of Blake Temple's type. We begin with the case p = 3 and show, under more or less technical assumptions, that the approximate solutions (u) given either by the vanishing viscosity method or by the Godunov scheme converge to weak entropy solutions as ε goes to 0. The first step consists...

Stability of periodic waves in Hamiltonian PDEs

Sylvie Benzoni-Gavage;  Pascal Noble;  L. Miguel Rodrigues — 2013

Journées Équations aux dérivées partielles

Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability  - in fact, stability, since we are dealing...

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