相关论文: Pointwise Green function bounds and stability of c…
We establish sharp pointwise Green's function bounds and consequent linearized and nonlinear stability for smooth traveling front solutions, or relaxation shocks, of general hyperbolic relaxation systems of dissipative type, under the…
In the previous paper \cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\bar u$ of a system of reaction diffusion equations, and also obtained…
Continuing the program initiated by Humpherys, Lyng, & Zumbrun [17] for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analyze the spectral stability of weak detonation waves in a…
Using analytical and numerical Evans-function techniques, we examine the spectral stability of strong-detonation-wave solutions of Majda's scalar model for a reacting gas mixture with an Arrhenius-type ignition function. We introduce an…
Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier--Stokes…
It has long been a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the principal aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such…
Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following the work…
Using pointwise semigroup techniques of Zumbrun--Howard and Mascia--Zumbrun, we obtain sharp global pointwise Green function bounds for noncharacteristic boundary layers of arbitrary amplitude. These estimates allow us to analyze linearized…
Using Evans function techniques, we develop a stability index for weak and strong detonation waves analogous to that developed for shock waves in [GZ,BSZ], yielding useful necessary conditions for stability. Here, we carry out the analysis…
Combining pointwise Green's function bounds obtained in a companion paper [MZ.2] with earlier, spectral stability results obtained in [HuZ], we establish nonlinear orbital stability of small amplitude viscous shock profiles for the class of…
For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions…
Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier--Stokes shocks…
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 $d=1,2$,…
By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier--Stokes equations with $\gamma$-law pressure (i) in the limit as…
In this paper, we investigate and prove the nonlinear stability of viscous shock wave solutions of a scalar viscous conservation law, using the methods developed for general systems of conservation laws by Howard, Mascia, Zumbrun and…
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…
In previous work \cite{W-Y-Z-local}, we studied the local well-posedness of weak solution to the 1-D full compressible Navier-Stokes equation with initial data of small total variation. Specifically, the local existence, the regularity, and…
In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system…
In this paper, we are concerned with the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The asymptotic stability of the steady state with the…
By working with the periodic resolvent kernel and Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction diffusion…