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Title: Parabolic PDEs on evolving spaces
Author: Alphonse, Amal
ISNI:       0000 0004 5916 0172
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2016
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This thesis is concerned with the well-posedness of solutions to certain linear and nonlinear parabolic PDEs on evolving spaces. We first present an abstract framework for the formulation and well-posedness of linear parabolic PDEs on abstract evolving Hilbert spaces. We introduce new function spaces and a notion of a weak time derivative called the weak material derivative for this purpose. We apply this general theory to moving hypersurfaces and Sobolev spaces and study four different linear problems including a coupled bulk-surface system and a dynamical boundary problem. Then we formulate a Stefan problem itself on an evolving surface and consider weak solutions given integrable data through the enthalpy approach, using a generalisation to the Banach space setting of the function spaces introduced in the abstract framework. We finish by studying a nonlocal problem: a porous medium equation with a fractional diffusion posed on an evolving surface and we prove well-posedness for bounded initial data.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics