Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.640984
Title: A parabolic PDE on an evolving curve and surface with finite time singularity
Author: Scott, Michael R.
ISNI:       0000 0004 5349 7911
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2014
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Abstract:
We consider the heat equation ∂∙tu + u∇M(t) . v - ∆M(t)u = 0 u(x,0) = u0 x ∈ M(0) on an evolving curve which forms a "kink" in finite time. We describe the behaviour of the solution at the singularity and look to continue the solution past the singularity. We perturb the heat equation and study the effects of a deterministic perturbation and a stochastic perturbation on the solution, before the singularity. We then consider the heat equation on an evolving surface that forms a "cone" singularity in finite time and study the behaviour of the solution at the singularity. We then look to continue the solution past the singularity, in some probabilistic sense. Finally, we consider the heat equation on an evolving curve, where the evolution of the curve is coupled to the solution of the equation on the curve. We prove existence and uniqueness of the solution for small times, before any singularity can occur.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC) [EP/HO23364/1]
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.640984  DOI: Not available
Keywords: QA Mathematics
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