Pointwise stability estimates for periodic traveling wave solutions of\n systems of viscous conservation laws

2012/10/12 by Soyeun Jung, Jung, Soyeun
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1210.3626

openalex publication_date 2012/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the previous paper citeJ1, we established pointwise bounds for the\nGreen function of the linearized equation associated with spatially periodic\ntraveling waves u of a system of reaction diffusion equations, and also\nobtained pointwise nonlinear stability and behavior of u under small\nperturbations. In this paper, using periodic resolvent kernels and the\nBloch-decomposition, we establish pointwise bounds for the Green function of\nthe linearized equation associated with periodic standing waves u of a\nsystem of conservation laws. We also show pointwise nonlinear stability of\n u by estimating decay of modulated perturbation v of u under\nsmall perturbation |v₀| \≤ E₀(1+|x|)^-3/2 for sufficiently small\nE₀>0.\n

Related

• Nonlinear stability of periodic traveling wave solutions of viscous conservation laws in dimensions one and two
• Pointwise asymptotic behavior of modulated periodic reaction-diffusion\n waves
• Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case
• Behavior of periodic solutions of viscous conservation laws under\n localized and nonlocalized perturbations
• Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems