Travelling waves for adaptive grid discretizations of reaction diffusion systems. I: Well-posedness
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Publication:2134148
DOI10.1007/s10884-021-10013-5zbMath1497.34108OpenAlexW3181839787WikidataQ115383158 ScholiaQ115383158MaRDI QIDQ2134148
Hermen Jan Hupkes, Erik S. Van Vleck
Publication date: 6 May 2022
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10884-021-10013-5
Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Traveling wave solutions (35C07) Lattice functional-differential equations (34K31)
Related Items (3)
Travelling waves for adaptive grid discretizations of reaction diffusion systems. II: Linear theory ⋮ Travelling waves for adaptive grid discretizations of reaction diffusion systems. III: Nonlinear theory ⋮ Traveling Waves for Spatially Discrete Systems of FitzHugh--Nagumo Type with Periodic Coefficients
Cites Work
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- Travelling waves for complete discretizations of reaction diffusion systems
- Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system
- Large time behavior of disturbed planar fronts in the Allen-Cahn equation
- Fast and slow waves in the FitzHugh-Nagumo equation
- Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations
- Traveling waves in discrete periodic media for bistable dynamics
- Existence of traveling wavefront solutions for the discrete Nagumo equation
- Weighted norms for the stability of traveling waves
- A geometric approach to singular perturbation problems with applications to nerve impulse equations
- The approach of solutions of nonlinear diffusion equations to travelling front solutions
- On travelling wave solutions of the Hodgkin-Huxley equations
- Multidimensional nonlinear diffusion arising in population genetics
- Traveling waves in lattice dynamical systems
- Numerical solution of Fisher's equation using a moving mesh method
- The global structure of traveling waves in spatially discrete dynamical systems
- Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
- Moving mesh methods based on moving mesh partial differential equations
- Maximum principles for discrete and semidiscrete reaction-diffusion equation
- Anisotropy, propagation failure, and wave speedup in traveling waves of discretizations of a Nagumo PDE
- Stability of radially symmetric travelling waves in reaction-diffusion equations
- A discrete convolution model for phase transitions
- Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
- Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions
- One-way hash function construction based on 2D coupled map lattices
- Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System
- Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations
- Long-Time Behavior of a Class of Biological Models
- Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons
- Bistable traveling waves around an obstacle
- Adaptivity with moving grids
- Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
- Propagation and Its Failure in Coupled Systems of Discrete Excitable Cells
- Analysis of Optimal Finite-Element Meshes in R 1
- Moving Mesh Techniques Based upon Equidistribution, and Their Stability
- Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
- A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
- The chemical basis of morphogenesis
- On the mesh nonsingularity of the moving mesh PDE method
- Moving Mesh Methods for Problems with Blow-Up
- Dynamics of monotone travelling fronts for discretizations of Nagumo PDEs
- Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model
- On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
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