Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches
We study seawater intrusion problems in confined and unconfined aquifers. We compare from a mathematical point of view the sharp interface approach with the sharp-diffuse interface approach. We demonstrate that, if the diffuse interface allows to establish a more efficient and logical maximum pr...
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Texas State University
2015-05-01
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doaj-dff9bfbed3dc4356aeedcd832c13b5d52020-11-24T23:35:52ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-05-012015126,127Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approachesCatherine Choquet0Ji Li1Carole Rosier2 Univ. La Rochelle, France Univ. Lille Nord de France, France Univ. Lille Nord de France, France We study seawater intrusion problems in confined and unconfined aquifers. We compare from a mathematical point of view the sharp interface approach with the sharp-diffuse interface approach. We demonstrate that, if the diffuse interface allows to establish a more efficient and logical maximum principle in the unconfined case, this advantage fails in the confined case. Problems can be formulated as strongly coupled systems of partial differential equations which include elliptic and parabolic equations (that can be degenerate), the degeneracy appearing only in the sharp interface case. Global in time existence results of weak solutions are established under realistic assumptions on the data.http://ejde.math.txstate.edu/Volumes/2015/126/abstr.htmlSeawater intrusion problemsharp-diffuse interfaceexistencestrongly coupled system elliptic - degenerate parabolic equations |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Catherine Choquet Ji Li Carole Rosier |
spellingShingle |
Catherine Choquet Ji Li Carole Rosier Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches Electronic Journal of Differential Equations Seawater intrusion problem sharp-diffuse interface existence strongly coupled system elliptic - degenerate parabolic equations |
author_facet |
Catherine Choquet Ji Li Carole Rosier |
author_sort |
Catherine Choquet |
title |
Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches |
title_short |
Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches |
title_full |
Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches |
title_fullStr |
Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches |
title_full_unstemmed |
Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches |
title_sort |
global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2015-05-01 |
description |
We study seawater intrusion problems in confined and unconfined aquifers.
We compare from a mathematical point of view the sharp interface approach
with the sharp-diffuse interface approach. We demonstrate that,
if the diffuse interface allows to establish a more efficient and logical
maximum principle in the unconfined case, this advantage fails in the
confined case.
Problems can be formulated as strongly coupled systems of partial
differential equations which include elliptic and parabolic equations
(that can be degenerate), the degeneracy appearing only in the sharp interface
case. Global in time existence results of weak solutions are established
under realistic assumptions on the data. |
topic |
Seawater intrusion problem sharp-diffuse interface existence strongly coupled system elliptic - degenerate parabolic equations |
url |
http://ejde.math.txstate.edu/Volumes/2015/126/abstr.html |
work_keys_str_mv |
AT catherinechoquet globalexistenceforseawaterintrusionmodelscomparisonbetweensharpinterfaceandsharpdiffuseinterfaceapproaches AT jili globalexistenceforseawaterintrusionmodelscomparisonbetweensharpinterfaceandsharpdiffuseinterfaceapproaches AT carolerosier globalexistenceforseawaterintrusionmodelscomparisonbetweensharpinterfaceandsharpdiffuseinterfaceapproaches |
_version_ |
1725524353583415296 |