Nonlinear stability of time-periodic viscous shocks

DOI10.1007/s00205-009-0274-1zbMath1221.35054arXiv0810.0498OpenAlexW3104386349WikidataQ60143884 ScholiaQ60143884MaRDI QIDQ982307

Margaret Beck, Kevin Zumbrun, Björn Sandstede

Publication date: 6 July 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.0498

zbMATH Keywords

Evans functionexponential dichotomyspatial dynamicsspectral stabilitypointwise boundsFloquet spectrumLax shock waves

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Stability in context of PDEs (35B35) Shock waves and blast waves in fluid mechanics (76L05) Initial value problems for second-order parabolic systems (35K45) Semilinear parabolic equations (35K58)

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Cites Work

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• Relative Poincaré-Hopf bifurcation and galloping instability of traveling waves
• Relative morse indices, Fredholm indices, and group velocities
• Galloping instability of viscous shock waves
• Hopf bifurcation of viscous shock waves in compressible gas dynamics and MHD
• Stability of undercompressive viscous shock profiles of hyperbolic-parabolic systems
• Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
• Pointwise Green function bounds for shock profiles of systems with real viscosity
• Elliptic partial differential equations of second order
• Refined wave-tracking and nonlinear stability of viscous Lax shocks
• Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations
• Stability of large-amplitude viscous shock profiles of hyperbolic-parabolic systems
• On nonlinear stability of general undercompressive viscous shock waves
• Time asymptotics of the Schrödinger wave function in time-periodic potentials
• Stability of undercompressive shock profiles
• Linear and quasilinear elliptic equations
• Evans functions for periodic waves on infinite cylindrical domains
• On the Structure of Spectra of Modulated Travelling Waves
• Hopf Bifurcation From Viscous Shock Waves
• Pointwise semigroup methods and stability of viscous shock waves
• Exponential dichotomies for linear non-autonomous functional differential equations of mixed type
• Nonlinear Stability of Semidiscrete Shock Waves
• Numerical Computation of Solitary Waves in Infinite Cylindrical Domains
• Spectral stability of modulated travelling waves bifurcating near essential instabilities
• Defects in Oscillatory Media: Toward a Classification
• Spinning instability of gaseous detonations
• MIXED-TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS, HOLOMORPHIC FACTORIZATION, AND APPLICATIONS
• L^p ASYMPTOTIC BEHAVIOR OF PERTURBED VISCOUS SHOCK PROFILES

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