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Thesis

On the geometric and analytic properties of some random fractals

Abstract:

The heat content of a domain D of ℝd is defined as

E(s) = ∫D u(s,x)dx,

where u is the solution to the heat equation with zero initial condition and unit Dirichlet boundary condition. This thesis studies the behaviour of E(s) for small s with a particular emphasis on the case where $D$ is a planar domain whose boundary is a random Koch curve.

When ∂D is spatially homogeneous, we show th...

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Institution:
University of Oxford
Oxford college:
Lincoln College
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute

Contributors

Role:
Supervisor
Publication date:
2014
Type of award:
DPhil
Level of award:
Doctoral
URN:
uuid:a9bbee2c-9958-464a-ac9e-bb8c42e107ea
Local pid:
ora:12474

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