Stability of Planar Waves in the Allen–Cahn Equation
From MaRDI portal
Publication:3643221
DOI10.1080/03605300902963500zbMath1191.35053OpenAlexW1994151612MaRDI QIDQ3643221
Masaharu Taniguchi, Hiroshi Matano, Mitsunori Nara
Publication date: 10 November 2009
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03605300902963500
asymptotic stabilityalmost periodicAllen-Cahn equationplanar wavealmost periodic perturbationsdecaying perturbations
Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57)
Related Items (45)
Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection ⋮ Multi-dimensional stability of waves travelling through rectangular lattices in rational directions ⋮ Stability of planar waves in a Lotka-Volterra system ⋮ Nontrivial dynamics beyond the logarithmic shift in two-dimensional Fisher-KPP equations ⋮ Stability of planar waves in the buffered bistable system ⋮ V-shaped traveling fronts of fractional Allen–Cahn equations ⋮ Traveling wave front and stability as planar wave of reaction diffusion equations with nonlocal delays ⋮ Spreading sets and one-dimensional symmetry for reaction-diffusion equations ⋮ Stability of planar traveling fronts in bistable reaction-diffusion systems ⋮ Multidimensional stability of planar traveling waves for the delayed nonlocal dispersal competitive Lotka-Volterra system ⋮ Stability of Front Solutions of the Bidomain Allen–Cahn Equation on an Infinite Strip ⋮ Stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term ⋮ Planar Propagating Terraces and the Asymptotic One-dimensional Symmetry of Solutions of Semilinear Parabolic Equations ⋮ Bistable transition fronts in \(\mathbb{R}^N\) ⋮ Large time behavior of the solutions with spreading fronts in the Allen-Cahn equations on \(\mathbb{R}^n\) ⋮ Pushed fronts of monostable reaction-diffusion-advection equations ⋮ Large time behavior of disturbed planar fronts in the Allen-Cahn equation ⋮ Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation ⋮ Fast propagation for KPP equations with slowly decaying initial conditions ⋮ Sharp relaxation rates for plane waves of general reaction-diffusion models ⋮ Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on \(\mathbb{R}^n\) ⋮ Nonlinear stability of traveling wavefronts for competitive-cooperative Lotka-Volterra systems of three species ⋮ Multidimensional stability of traveling fronts in combustion and non-KPP monostable equations ⋮ Time-periodic planar fronts around an obstacle ⋮ A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities ⋮ Entire solutions for bistable lattice differential equations with obstacles ⋮ Traveling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front ⋮ A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities in a channel with decreasing cross section ⋮ Multidimensional stability of time-periodic planar traveling fronts in bistable reaction-diffusion equations ⋮ Multidimensional stability of V-shaped traveling fronts in time periodic bistable reaction-diffusion equations ⋮ Stability of planar travelling waves for bistable reaction–diffusion equations in multiple dimensions ⋮ Multidimensional stability of disturbed pyramidal traveling fronts in the Allen-Cahn equation ⋮ Symmetry of traveling wave solutions to the Allen-Cahn equation in \({\mathbb R^{2}}\) ⋮ A variational approach to three-phase traveling waves for a gradient system ⋮ The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations ⋮ Lyapunov stability of planar waves to the reaction-diffusion equation with a non-Lipschitzian reaction term ⋮ Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations ⋮ Stability of planar waves in mono-stable reaction-diffusion equations ⋮ Stability of planar waves in reaction-diffusion system ⋮ Global asymptotic stability of traveling waves to the Allen-Cahn equation with a fractional Laplacian ⋮ Stability of Front Solutions of the Bidomain Equation ⋮ Planar waves of the buffered bistable system ⋮ MULTIDIMENSIONAL STABILITY OF PLANAR WAVES FOR DELAYED REACTION-DIFFUSION EQUATION WITH NONLOCAL DIFFUSION ⋮ The stability of traveling waves for Allen–Cahn equations with fractional Laplacian ⋮ Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The condition on the stability of stationary lines in a curvature flow in the whole plane
- The approach of solutions of nonlinear diffusion equations to travelling front solutions
- Local behavior of solutions of quasilinear parabolic equations
- Multidimensional Stability of Traveling Waves in a Bistable Reaction–Diffusion Equation, I
- Multidimensional Stability of Traveling Waves in a Bistable Reaction–Diffusion Equation, II
- Multidimensional stability of planar travelling waves
This page was built for publication: Stability of Planar Waves in the Allen–Cahn Equation
