A bifurcation approach to non‐planar traveling waves in reaction‐diffusion systems

DOI10.1002/gamm.200790012zbMath1133.35385OpenAlexW2044331732MaRDI QIDQ5424235

Arnd Scheel, Mariana Haragus

Publication date: 5 November 2007

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/gamm.200790012

zbMATH Keywords

stabilityBurgers equationsanisotropyviscous conservation lawscorner defectscorners in interaction interfaces

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Reaction-diffusion equations (35K57) Anisotropy in solid mechanics (74E10) Inhomogeneity in solid mechanics (74E05) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)

Related Items

Existence, uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems ⋮ Contact angle selection for interfaces in growing domains ⋮ Curved fronts in the Belousov-Zhabotinskii reaction-diffusion systems in \(\mathbb{R}^2\) ⋮ Global stability of curved fronts in the Belousov-Zhabotinskii reaction-diffusion system in \(\mathbb{R}^2\) ⋮ Stability of pyramidal traveling fronts in the degenerate monostable and combustion equations. II. ⋮ Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations ⋮ On the existence of axisymmetric traveling fronts in Lotka-Volterra competition-diffusion systems in \(\mathbb{R}^3\) ⋮ Spectrum of non-planar traveling waves ⋮ Uniqueness and global stability of V-shaped fronts for the buffered bistable system in \(\mathbb{R}^2\) ⋮ Spots and stripes in nonlinear Schrödinger-type equations with nearly one-dimensional potentials

Cites Work

• Oscillatory integrals and phenomena beyond all algebraic orders with applications to homoclinic orbits in reversible systems
• Stable viscous shocks in elliptic conservation laws
• Unnamed Item

This page was built for publication: A bifurcation approach to non‐planar traveling waves in reaction‐diffusion systems