Bernoulli Variational Problem and Beyond

Handle URI:
http://hdl.handle.net/10754/563150
Title:
Bernoulli Variational Problem and Beyond
Authors:
Lorz, Alexander; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Perthame, Benoît
Abstract:
The question of 'cutting the tail' of the solution of an elliptic equation arises naturally in several contexts and leads to a singular perturbation problem under the form of a strong cut-off. We consider both the PDE with a drift and the symmetric case where a variational problem can be stated. It is known that, in both cases, the same critical scale arises for the size of the singular perturbation. More interesting is that in both cases another critical parameter (of order one) arises that decides when the limiting behaviour is non-degenerate. We study both theoretically and numerically the values of this critical parameter and, in the symmetric case, ask if the variational solution leads to the same value as for the maximal solution of the PDE. Finally we propose a weak formulation of the limiting Bernoulli problem which incorporates both Dirichlet and Neumann boundary condition. © 2013 Springer-Verlag Berlin Heidelberg.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis
Issue Date:
17-Dec-2013
DOI:
10.1007/s00205-013-0707-8
Type:
Article
ISSN:
00039527
Sponsors:
The authors wish to thank the Fondation Sciences Mathematiques de Paris for the support of AL and PM. The authors also thank Frederic Hecht for his decisive advice on the numerics based on FreeFEM++.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLorz, Alexanderen
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorPerthame, Benoîten
dc.date.accessioned2015-08-03T11:36:57Zen
dc.date.available2015-08-03T11:36:57Zen
dc.date.issued2013-12-17en
dc.identifier.issn00039527en
dc.identifier.doi10.1007/s00205-013-0707-8en
dc.identifier.urihttp://hdl.handle.net/10754/563150en
dc.description.abstractThe question of 'cutting the tail' of the solution of an elliptic equation arises naturally in several contexts and leads to a singular perturbation problem under the form of a strong cut-off. We consider both the PDE with a drift and the symmetric case where a variational problem can be stated. It is known that, in both cases, the same critical scale arises for the size of the singular perturbation. More interesting is that in both cases another critical parameter (of order one) arises that decides when the limiting behaviour is non-degenerate. We study both theoretically and numerically the values of this critical parameter and, in the symmetric case, ask if the variational solution leads to the same value as for the maximal solution of the PDE. Finally we propose a weak formulation of the limiting Bernoulli problem which incorporates both Dirichlet and Neumann boundary condition. © 2013 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipThe authors wish to thank the Fondation Sciences Mathematiques de Paris for the support of AL and PM. The authors also thank Frederic Hecht for his decisive advice on the numerics based on FreeFEM++.en
dc.publisherSpringer Natureen
dc.titleBernoulli Variational Problem and Beyonden
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalArchive for Rational Mechanics and Analysisen
dc.contributor.institutionCNRS UMR 7598, Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, 4, pl. Jussieu F75252, Paris Cedex 05, Franceen
dc.contributor.institutionINRIA-Rocquencourt, EPI BANG, Paris, Franceen
kaust.authorMarkowich, Peter A.en
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