Invariant regions and asymptotic bounds for a hyperbolic version of the nerve equation

DOI10.1016/0362-546X(91)90105-AzbMath0754.92004OpenAlexW2013153859MaRDI QIDQ3978489

Marta València

Publication date: 25 June 1992

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(91)90105-a

zbMATH Keywords

semilinear wave equationexistenceuniquenessinitial value problemparabolic equationnonlinear dampingFitzHugh-Nagumo equationsnerve conductionconstant steady state solutionscontractiveness-propertypositively invariant rectangular regions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Second-order nonlinear hyperbolic equations (35L70)

Cites Work

• Unnamed Item
• Qualitative theory of the Fitz Hugh-Nagumo equations
• Numerical studies of the steady-state equations for a Hodgkin-Huxley model
• Non-linear semi-groups
• On invariant regions and asymptotic bounds for semilinear partial differential equations

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