Existence and Nonexistence of Traveling Wave Solutions for a Bistable Reaction-Diffusion Equation in an Infinite Cylinder Whose Diameter is Suddenly Increased

DOI10.1080/03605300500300006zbMath1087.35052OpenAlexW2113997043MaRDI QIDQ5713479

Emmanuel Grenier, Guillemette Chapuisat

Publication date: 14 December 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500300006

zbMATH Keywords

Green's functionNeumann's boundary conditionsswitch waveswave extinction

Mathematics Subject Classification ID

Related Items (17)

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Cites Work

• Unnamed Item
• Unnamed Item
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Reaction-diffusion problems in cylinders with no invariance by translation. I: Small perturbations
• Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders
• Reaction-diffusion problems in cylinders with no invariance by translation. II: Monotone perturbations
• Elliptic partial differential equations of second order

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