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Parabolic type equations associated with the Dirichlet form on the Sierpinski gasket

Abstract:

By using analytic tools from stochastic analysis, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along fractals (which can be considered as models of simplified rough porous media). Unlike the regular space case, such parabolic type equations involving non-linear convection terms must take a different form, due to the fact that convection terms must be singular to the “linear part” which defines the heat semigroup. In or...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00440-019-00910-8

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Exeter College
Role:
Author
Publisher:
Springer Publisher's website
Journal:
Probability Theory and Related Fields Journal website
Volume:
175
Issue:
3-4
Pages:
1063–1098
Publication date:
2019-04-04
Acceptance date:
2019-03-24
DOI:
EISSN:
1432-2064
ISSN:
0178-8051
Source identifiers:
984166
Language:
English
Keywords:
Pubs id:
pubs:984166
UUID:
uuid:89076fb6-e81c-48b7-bcf4-61aa1b50b311
Local pid:
pubs:984166
Deposit date:
2019-03-24

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