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An abstract framework for parabolic PDEs on evolving spaces
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Alphonse, Amal, Elliott, Charles M. and Stinner, Björn (2015) An abstract framework for parabolic PDEs on evolving spaces. Portugaliae Mathematica, 72 (1). pp. 1-46. doi:10.4171/PM/1955 ISSN 0032-5155.
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Official URL: http://dx.doi.org/10.4171/PM/1955
Abstract
We present an abstract framework for treating the theory of well-posedness of solutions to abstract parabolic partial di¤erential equations on evolving Hilbert spaces. This theory is applicable to variational formulations of PDEs on evolving spatial domains including moving hypersurfaces. We formulate an appropriate time derivative on evolving spaces called the material derivative and define a weak material derivative in analogy with the usual time derivative in fixed domain problems; our setting is abstract and not restricted to evolving domains or surfaces. Then we show well-posedness to a certain class of parabolic PDEs under some assumptions on the parabolic operator and the data.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Portugaliae Mathematica | ||||
Publisher: | European Mathematical Society Publishing House | ||||
ISSN: | 0032-5155 | ||||
Official Date: | 2015 | ||||
Dates: |
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Volume: | 72 | ||||
Number: | 1 | ||||
Page Range: | pp. 1-46 | ||||
DOI: | 10.4171/PM/1955 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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