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7 papers · 2 filters
Instabilities in Zakharov Equations for Laser Propagation in a Plasma
Thierry Colin, Guy Metivier
F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for…
Remarks on the Well-Posedness of the Nonlinear Cauchy Problem
Guy Metivier
We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions…
The Cauchy Problem for Wave Equations with NonLipschitz Coefficients
Ferruccio Colombini, Guy Metivier
In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only "Log-Lip…
Global existence and uniqueness for the Lake equations with vanishing topography : elliptic estimates for degenerate equations
Bresch Didier, Guy Metivier
This paper deals with global existence and uniqueness for the lake equations with a bottom topography vanishing on the shore. Our result generalizes previous studies that assumed t…
Nonclassical multidimensional viscous and inviscid shocks
Olivier Gues, Guy Métivier, Mark Williams +1
Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosi…
Viscous Boundary Value Problems for Symmetric Systems with Variable Multiplicities
Olivier Gues, Guy Métivier, Mark Williams +1
Extending investigations of Métivier&Zumbrun in the hyperbolic case, we treat stability of viscous shock and boundary layers for viscous perturbations of multidimensional hyperboli…