Analytical and numerical investigation of traveling waves for the Allen–Cahn model with relaxation

DOI10.1142/S0218202516500226zbMath1337.35022arXiv1410.1659OpenAlexW2951156210MaRDI QIDQ2799319

Corrado Lattanzia, Corrado Mascia, Ramón G. Plaza, Chiara Simeoni

Publication date: 8 April 2016

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1659

zbMATH Keywords

nonlinear stabilityrelaxation relation of Cattaneo-Maxwell type

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) First-order hyperbolic systems (35L40) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Traveling wave solutions (35C07)

Related Items (10)

Motion of interfaces for a damped hyperbolic Allen-Cahn equation ⋮ Computation and Stability of Traveling Waves in Second Order Evolution Equations ⋮ Unnamed Item ⋮ Exact representation of the asymptotic drift speed and diffusion matrix for a class of velocity-jump processes ⋮ Spectral instability of small-amplitude periodic waves for hyperbolic non-Fickian diffusion advection models with logistic source ⋮ Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation ⋮ Slow motion for a hyperbolic variation of Allen–Cahn equation in one space dimension ⋮ Traveling wave solutions of partial differential equations via neural networks ⋮ Kinetic schemes for assessing stability of traveling fronts for the Allen-Cahn equation with relaxation ⋮ Unnamed Item

Cites Work

• Analytical and numerical solutions of the density dependent Nagumo telegraph equation
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• A stochastic model related to the telegrapher's equation
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Dichotomies in stability theory
• Mathematical biology. Vol. 1: An introduction.
• Analytic and approximate solutions for Nagumo telegraph reaction diffusion equation
• Spectral and dynamical stability of nonlinear waves
• Hyperbolic travelling fronts
• Global stability of travelling fronts for a damped wave equation with bistable nonlinearity
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• One-Parameter Semigroups for Linear Evolution Equations
• Heat waves
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Analytical and numerical investigation of traveling waves for the Allen–Cahn model with relaxation