Catherine Choquet, Ji Li, Carole Rosier
Abstract:
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.
Submitted April 2, 2015. Published May 6, 2015.
Math Subject Classifications: 35R35, 35K20, 35J60, 76S05, 76T05.
Key Words: Seawater intrusion problem; sharp-diffuse interface; existence;
strongly coupled system; elliptic - degenerate parabolic equations.
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Catherine Choquet Univ. La Rochelle, MIA Avenue M. Crépeau, F-17042 La Rochelle, France email: cchoquet@univ-lr.fr |
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Ji Li Univ. Lille Nord de France F-59000, Lille, France email: ji.li@lmpa.univ-littoral.fr |
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Carole Rosier Univ. Lille Nord de France F-59000, Lille, France email: rosier@lmpa.univ-littoral.fr |
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