Abstract
Language  English 

Qualification  Ph.D. 
Awarding Institution 

Supervisors/Advisors 

Award date  30 Apr 2013 
Status  Unpublished  2013 
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Travelling waves in heterogeneous media. / Boden, Adam.
2013.Research output: Thesis › Doctoral Thesis
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TY  THES
T1  Travelling waves in heterogeneous media
AU  Boden,Adam
PY  2013
Y1  2013
N2  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 analysing the bifurcations in this case we are able to find travelling wave solutions with periodic and homoclinic structures. Finally we examine what happens to the travelling wave solutions as the period of the periodic dependence in the nonlinearity tends to zero.
AB  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 analysing the bifurcations in this case we are able to find travelling wave solutions with periodic and homoclinic structures. Finally we examine what happens to the travelling wave solutions as the period of the periodic dependence in the nonlinearity tends to zero.
M3  Doctoral Thesis
ER 