Low-frequency stability analysis of periodic traveling-wave solutions of viscous conservation laws in several dimensions

DOI10.4171/ZAA/1275zbMath1099.35014arXivmath/0510515OpenAlexW2012536848MaRDI QIDQ2492112

Myunghyun Oh, Kevin Zumbrun

Publication date: 6 June 2006

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510515

zbMATH Keywords

low-frequency dispersion relationpartial justification of the WKB expansion

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Hyperbolic conservation laws (35L65) General spectral theory of ordinary differential operators (34L05) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20)

Related Items (14)

\(L^1\)-stability of periodic stationary solutions of scalar convection-diffusion equations ⋮ On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions ⋮ Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations ⋮ Large-amplitude modulation of periodic traveling waves ⋮ Rigorous justification of the Whitham modulation equations for equations of Whitham type ⋮ Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability ⋮ Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves ⋮ Pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation laws ⋮ Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation ⋮ Numerical survey on hyperbolicity of the homogenized equation for van der Waals gas in Eulerian coordinates ⋮ Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions ⋮ Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case ⋮ The modulational instability for a generalized Korteweg-de Vries equation ⋮ About plane periodic waves of the nonlinear Schrödinger equations

Cites Work

• Stability of periodic solutions of conservation laws with viscosity: analysis of the Evans function
• Stability of periodic solutions of conservation laws with viscosity: Pointwise bounds on the Green function
• Existence and stability of multidimensional shock fronts in the vanishing viscosity limit
• Entropy of the liquid-vapour mixture of a thermo-capillary fluid
• On the structure of the spectra of periodic travelling waves
• Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability
• Multidimensional viscous shocks II: The small viscosity limit
• Spectral Stability of Periodic Solutions of Viscous Conservation Laws: Large Wavelength Analysis
• Viscous and inviscid stability of multidimensional planar shock fronts

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