Reaction and Diffusion on the Sierpinski Gasket

Riley, Caroline J. (2006) Reaction and Diffusion on the Sierpinski Gasket. Doctoral thesis, The University of Manchester.

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Abstract

In this thesis we study non-linear dynamical systems on complex domains. Although the systems we consider are mathematical abstractions, our motivation is to gain insights into neurobiological systems. The mathematical techniques we employ concern analysis on a particular class of fractal sets. This theory allows one to construct a Laplacian and to study the spectrum and eigenfunctions given a variety of boundary conditions. This thesis uses these results to define and study the cable equation and the FitzHugh-Nagumo system on the Sierpinski Gasket.

Item Type: Thesis (Doctoral)
Additional Information: Dr. Riley worked with Prof. D. S. Broomhead.
Uncontrolled Keywords: Analysis on fractals, Sierpinski gasket, graph Laplacian, harmonic functions
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences
Depositing User: Dr Mark Muldoon
Date Deposited: 11 Jan 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/690

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