6 citations · 9 across the 4 of their papers we have counts for
4 papers
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…
Hopf bifurcation of viscous shock wave solutions of compressible Navier-Stokes equations and MHD
Benjamin Texier, Kevin Zumbrun
Extending our previous results for artificial viscosity systems, we show, under suitable spectral hypotheses, that shock wave solutions of compressible Navier--Stokes (cNS) and mag…
Galloping instability of viscous shock waves
Benjamin Texier, Kevin Zumbrun
Motivated by physical and numerical observations of time oscillatory ``galloping'', ``spinning'', and ``cellular'' instabilities of detonation waves, we study Poincaré--Hopf bifurc…
Pointwise Green function bounds and stability of combustion waves
Gregory Lyng, Mohammadreza Raoofi, Benjamin Texier +1
Generalizing similar results for viscous shock and relaxation waves, we establish sharp pointwise Green function bounds and linearized and nonlinear stability for traveling wave so…