dc.contributor.author Driver, David Philip dc.date.accessioned 2018-07-03T14:24:11Z dc.date.available 2018-07-03T14:24:11Z dc.date.issued 2018-07-21 dc.date.submitted 2017-09-29 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/277769 dc.description.abstract In this thesis, we study a class of reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{L}u + \phi u - \tfrac{1}{k} u^{k+1}$ where $\mathcal{L}$ is the stochastic generator of a Markov process, $\phi$ is a function of the space variables and $k\in \mathbb{R}\backslash\{0\}$. An important example, in the case when $k>0$, is equations of the FKPP-type. We also give an example from the theory of utility maximisation problems when such equations arise and in this case $k<0$. We introduce a new representation, for the solution of the equation, as the optimal value of an optimal control problem. We also give a second representation which can be seen as a dual problem to the first optimisation problem. We note that this is a new type of dual problem and we compare it to the standard Lagrangian dual formulation. By choosing controls in the optimisation problems we obtain upper and lower bounds on the solution to the PDE. We use these bounds to study the speed of the wave front of the PDE in the case when $\mathcal{L}$ is the generator of a suitable Lévy process. dc.description.sponsorship Research funded by EPSRC/CCA dc.language.iso en dc.rights All rights reserved dc.rights All Rights Reserved en dc.rights.uri https://www.rioxx.net/licenses/all-rights-reserved/ en dc.subject KPP dc.subject FKPP dc.subject Reaction-Diffusion Equations dc.subject Branching processes dc.subject Front Propagation dc.subject HJB Equation dc.subject Stochastic Optimisation dc.subject Travelling Waves dc.title An Optimisation-Based Approach to FKPP-Type Equations dc.type Thesis dc.type.qualificationlevel Doctoral dc.type.qualificationname Doctor of Philosophy (PhD) dc.publisher.institution University of Cambridge dc.publisher.department Cambridge Centre for Analysis (CCA) dc.date.updated 2018-07-03T13:56:12Z dc.identifier.doi 10.17863/CAM.25108 dc.contributor.orcid Driver, David Philip [0000-0002-4159-8120] dc.publisher.college Churchill College dc.type.qualificationtitle PhD in Mathematics cam.supervisor Tehranchi, Michael cam.thesis.funding true rioxxterms.freetoread.startdate 2018-07-03
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