Related papers: Stability of scalar radiative shock profiles
We study the propagation of ultra-short pulses in a cubic nonlinear medium. Using multiple-scale technique, we derive a new wave equation that preserves the nonlocal dispersion present in Maxwell's equations. As a result, we are able to…
The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…
This paper studies the asymptotic stability of solution to an initial-boundary value problem for a hyperbolic-elliptic coupled system on two-dimensional half space, where the data on the boundary and at the far field are prescribed as $u_-$…
By reduction to a generalized Sturm Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, over the full parameter range of their existence, for both…
This paper establishes the nonlinear time-asymptotic stability of shifted planar viscous shock waves for the three-dimensional relaxed compressible Navier-Stokes equations, in which a modified Maxwell-type model replaces the classical…
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…
In three dimensions, the parabolic-elliptic Keller-Segel system exhibits a rich variety of singularity formations. Notably, it admits an explicit self-similar blow-up solution whose radial stability, conjectured more than two decades ago in…
Using a combination of Kawashima- and Goodman-type energy estimates, we establish spectral stability of general small-amplitude relaxation shocks of symmetric dissipative systems. This extends previous results obtained by Plaza and Zumbrun…
Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
This paper develops the basic sets of equations which lead to the conservation laws describing collisionless plasma shock waves. We discuss the evolution of shock waves by wave steepening, derive the Rankine-Hugoniot conditions for…
In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
Extending results of Oh and Zumbrun in dimensions $d\ge 3$, we establish nonlinear stability and asymptotic behavior of spatially-periodic traveling-wave solutions of viscous systems of conservation laws in critical dimensions $d=1,2$,…
We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which…
We analyze the dynamical stability of black hole solutions in self-gravitating nonlinear electrodynamics with respect to arbitrary linear fluctuations of the metric and the electromagnetic field. In particular, we derive simple conditions…
We present a new method for analyzing the global stability of the Sedov-von Neumann-Taylor self-similar solutions, describing the asymptotic behavior of spherical decelerating shock waves, expanding into ideal gas with density \propto…
We establish the full asymptotic stability of solitary wave solutions for the 1D focusing cubic Schr\"odinger equation on the line under small perturbations in weighted Sobolev spaces, building upon our results in [58]. The proof integrates…
This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For the shock profile, we show that the solution approaches…