Bifurcation and stability of periodic traveling waves for a reaction- diffusion system

DOI10.1016/0022-0396(83)90075-XzbMath0494.35056MaRDI QIDQ1169098

David L. Barrow, Peter W. Bates

Publication date: 1983

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

traveling wave solutionsreaction-diffusion equationsbiological phenomena having excitable dynamicsHodgkin-Huxley equations of nerve conductions

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Bifurcations in context of PDEs (35B32)

Related Items (6)

Reaction-diffusion problems in cylinders with no invariance by translation. I: Small perturbations ⋮ Convergence to equilibrium in a reaction-diffusion system ⋮ Existence of solutions for a class of weakly coupled semilinear elliptic systems ⋮ Steady state solutions for certain reaction diffusion systems ⋮ Global bifurcation structure of a one-dimensional Ginzburg–Landau model ⋮ Travelling waves in radially symmetric parabolic systems

Cites Work

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• A semilinear parabolic system arising in the theory of superconductivity
• Geometric theory of semilinear parabolic equations
• On the stability of waves of nonlinear parabolic systems
• Bifurcation from simple eigenvalues
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†

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