The sub-supersolution method for the Fitzhugh-Nagumo type reaction-diffusion system with heterogeneity

DOI10.3934/dcds.2018101zbMath1415.34082OpenAlexW2791640358MaRDI QIDQ1661071

Takashi Kajiwara

Publication date: 16 August 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2018101

zbMATH Keywords

sub-supersolution methodheteroclinic solutionFitzHugh-Nagumo type reaction diffusion systems

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Variational methods for elliptic systems (35J50) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

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• Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional
• On stable nonconstant stationary solutions and mesoscopic patterns for FitzHugh-Nagumo equations in higher dimensions.
• A minimization problem associated with elliptic systems of FitzHugh--Nagumo type
• A heteroclinic solution to a variational problem corresponding to FitzHugh-Nagumo type reaction-diffusion system with heterogeneity
• Multiple stable patterns in a balanced bistable equation with heterogeneous environments
• Planar Standing Wavefronts in the FitzHugh--Nagumo Equations
• Stable transition layers in a balanced bistable equation

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