publication . Doctoral thesis . 2013

Travelling waves in heterogeneous media

Boden, Adam;
Restricted English
  • Published: 01 Jan 2013
  • Country: United Kingdom
Abstract
In this thesis we study the existence of travelling wave type solutions for a reaction diffusion equation in R2 with a nonlinearity which depends periodically on the spatial variable. Specifically we will consider a particular class of nonlinearities where we treat the coefficient of the linear term as a parameter. For this class of nonlinearities we formulate the problem as a spatial dynamical system and use a centre manifold reduction to find conditions on the parameter and nonlinearity for the existence of travelling wave type solutions with particular wave speeds. We then consider what happens if the parameter and the wave speed vary close to zero; by analys...
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