Travelling waves for adaptive grid discretizations of reaction diffusion systems. I: Well-posedness
type: Item
instance of: scholarly article
title: Travelling waves for adaptive grid discretizations of reaction diffusion systems. I: Well-posedness
zbMATH Open document ID: 1497.34108
author: H. J. Hupkes
author: E. Van Vleck
published in: Journal of Dynamics and Differential Equations
publication date: 2022-05-06T00:00:00Z
Mathematics Subject Classification ID: 34K31
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 7522537
zbMATH Keywords: travelling waves
zbMATH Keywords: adaptive grids
zbMATH Keywords: singular perturbations
zbMATH Keywords: spatial discretizations
Wikidata QID: Q115383158
MaRDI profile type: Publication
full work available at URL: s10884-021-10013-5
OpenAlex ID: W3181839787
cites work: Multidimensional nonlinear diffusion arising in population genetics
cites work: Analysis of Optimal Finite-Element Meshes in R 1
cites work: A discrete convolution model for phase transitions
cites work: On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
cites work: Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons
cites work: Bistable traveling waves around an obstacle
cites work: Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model
cites work: Moving Mesh Methods for Problems with Blow-Up
cites work: Adaptivity with moving grids
cites work: A geometric approach to singular perturbation problems with applications to nerve impulse equations
cites work: Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system
cites work: Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System
cites work: Traveling waves in discrete periodic media for bistable dynamics
cites work: Traveling waves in lattice dynamical systems
cites work: Q5669725
cites work: Anisotropy, propagation failure, and wave speedup in traveling waves of discretizations of a Nagumo PDE
cites work: Q4708886
cites work: Dynamics of monotone travelling fronts for discretizations of Nagumo PDEs
cites work: The approach of solutions of nonlinear diffusion equations to travelling front solutions
cites work: On travelling wave solutions of the Hodgkin-Huxley equations
cites work: Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations
cites work: On the mesh nonsingularity of the moving mesh PDE method
cites work: Moving mesh methods based on moving mesh partial differential equations
cites work: Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
cites work: Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations
cites work: Travelling waves for complete discretizations of reaction diffusion systems
cites work: Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
cites work: Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells
cites work: A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
cites work: Fast and slow waves in the FitzHugh-Nagumo equation
cites work: The global structure of traveling waves in spatially discrete dynamical systems
cites work: Large time behavior of disturbed planar fronts in the Allen-Cahn equation
cites work: Numerical solution of Fisher's equation using a moving mesh method
cites work: Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
cites work: Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
cites work: Moving Mesh Techniques Based upon Equidistribution, and Their Stability
cites work: Stability of radially symmetric travelling waves in reaction-diffusion equations
cites work: Weighted norms for the stability of traveling waves
cites work: Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions
cites work: Maximum principles for discrete and semidiscrete reaction-diffusion equation
cites work: The chemical basis of morphogenesis
cites work: One-way hash function construction based on 2D coupled map lattices
cites work: Q3910354
cites work: Long-Time Behavior of a Class of Biological Models
cites work: Existence of traveling wavefront solutions for the discrete Nagumo equation
DOI: 10.1007/S10884-021-10013-5
description: scientific article