Stability and freezing of nonlinear waves in first order hyperbolic PDEs

DOI10.1007/s10884-012-9241-xzbMath1252.35051OpenAlexW2044397518MaRDI QIDQ431118

Jens Rottmann-Matthes

Publication date: 26 June 2012

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-012-9241-x

zbMATH Keywords

Hodgkin-Huxley equationsfreezing methodnonlinear stability of a traveling waveunknown asymptotic phase

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Estimates of eigenvalues in context of PDEs (35P15) Initial value problems for first-order hyperbolic systems (35L45) Numerical nonlinear stabilities in dynamical systems (65P40) Traveling wave solutions (35C07)

Related Items (7)

Stability of Traveling Oscillating Fronts in Complex Ginzburg Landau Equations ⋮ On the spectral stability of standing waves of the one-dimensional \(M^5\)-model ⋮ Computation and Stability of Traveling Waves in Second Order Evolution Equations ⋮ Freezing similarity solutions in the multi-dimensional Burgers equation ⋮ Stability of a Planar Front in a Class of Reaction-Diffusion Systems ⋮ Computation and stability of waves in equivariant evolution equations ⋮ Spectrum of the M⁵-traveling waves

Uses Software

• MATCONT

Cites Work

• Linear stability of traveling waves in first-order hyperbolic PDEs
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• On a singular initial-boundary-value problem for a reaction-diffusion equation arising from a simple model of isothermal chemical autocatalysis
• The effects of weak hyperbolicity on the diffusion of heat
• One-Parameter Semigroups for Linear Evolution Equations
• Propagation of frontal polymerization—crystallization waves
• On the Convergence to Steady State of Solutions of Nonlinear Hyperbolic-Parabolic Systems
• Reduction and reconstruction for self-similar dynamical systems
• The evolution of travelling waves in the weakly hyperbolic generalized Fisher model
• Freezing Solutions of Equivariant Evolution Equations
• Heat waves
• MATCONT
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