The Origin of Wave Blocking for a Bistable Reaction-Diffusion Equation : A General Approach

The Origin of Wave Blocking for a Bistable Reaction-Diffusion Equation : A General Approach

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dc.contributor.author Roy, Christian
dc.date.accessioned 2012-04-12T17:16:27Z
dc.date.available 2012-04-12T17:16:27Z
dc.date.created 2012 en_US
dc.date.issued 2012-04-12
dc.identifier.uri http://hdl.handle.net/10393/22704
dc.description.abstract Mathematical models displaying travelling waves appear in a variety of domains. These waves are often faced with different kinds of perturbations. In some cases, these perturbations result in propagation failure, also known as wave-blocking. Wave-blocking has been studied in the case of several specific models, often with the help of numerical tools. In this thesis, we will display a technique that uses symmetry and a center manifold reduction to find a criterion which defines regions in parameter space where a wave will be blocked. We focus on waves with low velocity and small symmetry-breaking perturbations, which is where the blocking initiates; the organising center. The range of the tools used makes the technique easily generalizable to higher dimensions. In order to demonstrate this technique, we apply it to the bistable equation. This allows us to do calculations explicitly. As a result, we show that wave-blocking occurs inside a wedge originating from the organising center and derive an expression for this wedge to leading order. We verify our results with some numerical simulations. en_US
dc.language.iso en en_US
dc.subject Travelling wave en_US
dc.subject Bistable Equation en_US
dc.subject Center Manifold Reduction en_US
dc.subject Wave Blocking en_US
dc.subject Reaction Diffusion Equation en_US
dc.subject Organising Center en_US
dc.subject Symmetry en_US
dc.title The Origin of Wave Blocking for a Bistable Reaction-Diffusion Equation : A General Approach en_US
dc.type Thèse / Thesis en_US
dc.faculty.department Mathématiques et statistique / Mathematics and Statistics en_US
dc.contributor.supervisor LeBlanc, Victor
dc.embargo.terms immediate en_US
dc.degree.name MSc en_US
dc.degree.level masters en_US
dc.degree.discipline Sciences / Science en_US

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