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Parabolic PDEs on evolving spaces
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Alphonse, Amal (2016) Parabolic PDEs on evolving spaces. PhD thesis, University of Warwick.
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WRAP_THESIS_Alphonse_2016.pdf - Submitted Version - Requires a PDF viewer. Download (1120Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2863326~S1
Abstract
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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Differential equations, Parabolic | ||||
Official Date: | February 2016 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Stinner, Björn ; Elliott, Charlie | ||||
Extent: | x, 204 leaves | ||||
Language: | eng |
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