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A Stefan problem on an evolving surface
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Alphonse, Amal and Elliott, Charles M. (2015) A Stefan problem on an evolving surface. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373 (2050). doi:10.1098/rsta.2014.0279 ISSN 1364-503X.
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Official URL: http://dx.doi.org/10.1098/rsta.2014.0279
Abstract
We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L1 data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for Embedded Image data; this is done by regularization of the nonlinearity. The regularized problem is solved by a fixed point theorem and then uniform estimates are obtained in order to pass to the limit. By using a duality method, we show continuous dependence, which allows us to extend the results to L1 data.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Hypersurfaces | ||||||
Journal or Publication Title: | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||
Publisher: | The Royal Society Publishing | ||||||
ISSN: | 1364-503X | ||||||
Official Date: | 10 August 2015 | ||||||
Dates: |
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Volume: | 373 | ||||||
Number: | 2050 | ||||||
Number of Pages: | 21 | ||||||
DOI: | 10.1098/rsta.2014.0279 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Date of first compliant deposit: | 12 April 2018 | ||||||
Date of first compliant Open Access: | 12 April 2018 | ||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||
Grant number: | EP/H023364/1 (EPSRC) |
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