An application for an implicit function theorem of Craven and Nashed: continuum limits of lattice differential equations

DOI10.1016/J.JMAA.2010.01.043zbMATH Open1200.34009OpenAlexW2075029153MaRDI QIDQ968827

Andreas Johann

Publication date: 10 May 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.01.043

zbMATH Keywords

continuum limitimplicit function theoremtraveling wave solutionlattice differential equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07) Ordinary lattice differential equations (34A33)

Cites Work

• Title not available (Why is that?)
• A variant of Newton's method for the computation of traveling waves of bistable differential-difference equations
• Some threshold results for models of myelinated nerves
• Existence of traveling wavefront solutions for the discrete Nagumo equation
• The global structure of traveling waves in spatially discrete dynamical systems
• Generalized implicit function theorems when the derivative has no bounded inverse
• Dynamics of monotone travelling fronts for discretizations of Nagumo PDEs

Related Items (2)

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

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