Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves

DOI10.1016/j.physd.2017.12.003zbMath1380.65428arXiv1701.04289OpenAlexW2572725722MaRDI QIDQ1701303

Blake Barker, Kevin Zumbrun, Soyeun Jung

Publication date: 22 February 2018

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04289

zbMATH Keywords

conservation lawsTuring instabilitystable periodic waves

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Hyperbolic conservation laws (35L65) Bifurcations in context of PDEs (35B32) Numerical nonlinear stabilities in dynamical systems (65P40)

Related Items

Perturbation of the spectra for asymptotically constant differential operators and applications

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Cites Work

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• Quasi-gradient systems, modulational dichotomies, and stability of spatially periodic patterns.
• Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations
• Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow
• Computing spectra of linear operators using the Floquet-Fourier-Hill method
• SpectrUW: a laboratory for the numerical exploration of spectra of linear operators
• Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case
• Instability and stability of rolls in the Swift-Hohenberg equation
• 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
• Diffusive stability of spatially periodic solutions of the Brusselator model
• Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation
• Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability
• Low-frequency stability analysis of periodic traveling-wave solutions of viscous conservation laws in several dimensions
• Convergence of Hill's Method for Nonselfadjoint Operators
• On the convergence of Hill’s method
• Pattern formation with a conservation law
• The chemical basis of morphogenesis
• Spectral Stability of Periodic Solutions of Viscous Conservation Laws: Large Wavelength Analysis