7 citations · 26 across the 9 of their papers we have counts for
9 papers
On nonlinear stabilization of linearly unstable maps
Thierry Gallay, Benjamin Texier, Kevin Zumbrun
We examine the phenomenon of nonlinear stabilization, exhibiting a variety of related examples and counterexamples. For Gâteaux differentiable maps, we discuss a mechanism of nonli…
Approximations of pseudo-differential flows
Benjamin Texier
Given a classical symbol of order zero, and associated semiclassical operators we prove that the flow of is well approximat…
Entropy criteria and stability of extreme shocks: a remark on a paper of Leger and Vasseur
Benjamin Texier, Kevin Zumbrun
We show that a relative entropy condition recently shown by Leger and Vasseur to imply uniqueness and stable dependence on initial data of Lax 1- or -shock solutions of an…
Existence of quasilinear relaxation shock profiles
Guy Metivier, Benjamin Texier, Kevin Zumbrun
We establish existence with sharp rates of decay and distance from the Chapman--Enskog approximation of small-amplitude quasilinear relaxation shocks in the general case that the p…
Nash--Moser iteration and singular perturbations
Benjamin Texier, Kevin Zumbrun
We present a simple and easy-to-use Nash--Moser iteration theorem tailored for singular perturbation problems admitting a formal asymptotic expansion or other family of approximate…
Transition to longitudinal instability of detonation waves is generically associated with Hopf bifurcation to time-periodic galloping solutions
Benjamin Texier, Kevin Zumbrun
We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier--Stokes equations is generically associated with Hopf bifurcation…