4 citations · 8 across the 4 of their papers we have counts for
5 papers
On Métivier's Lax-Mizohata theorem and extensions to weak defects of hyperbolicity. Part two
Karim Ndoumajoud, Benjamin Texier
We continue our study of initial-value problems for fully nonlinear systems exhibiting strong or weak defects of hyperbolicity. We prove that, regardless of the initial Sobolev reg…
Space-time resonances and high-frequency Raman instabilities in the two-fluid Euler-Maxwell system
Eric Dumas, Yong Lu, Benjamin Texier
We show that space-time resonances induce high-frequency Raman instabilities in the two-fluid Euler-Maxwell system describing laser-plasma interactions. A consequence is that the Z…
On Métivier's Lax-Mizohata theorem and extensions to weak defects of hyperbolicity. Part one
Karim Ndoumajoud, Benjamin Texier
We prove that, for first-order, fully nonlinear systems of partial differential equations, under an hypothesis of ellipticity for the principal symbol, the Cauchy problem has no so…
The onset of instability in first-order systems
Nicolas Lerner, Toan T. Nguyen, Benjamin Texier
We study the Cauchy problem for first-order quasi-linear systems of partial differential equations. When the spectrum of the initial principal symbol is not included in the real li…
A stability criterion for high-frequency oscillations
Yong Lu, Benjamin Texier
We show that a simple Levi compatibility condition determines stability of WKB solutions to semilinear hyperbolic initial-value problems issued from highly-oscillating initial data…