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2007.6: Reaction and Diffusion on the Sierpinski Gasket

2007.6: Caroline J. Riley (2006) Reaction and Diffusion on the Sierpinski Gasket. PhD 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 (PhD)
Additional Information:

Dr. Riley worked with Prof. D. S. Broomhead.

Uncontrolled Keywords:Analysis on fractals, Sierpinski gasket, graph Laplacian, harmonic functions
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 58 Global analysis, analysis on manifolds
MSC 2000 > 92 Biology and other natural sciences
MIMS number:2007.6
Deposited By:Dr Mark Muldoon
Deposited On:11 January 2007

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