Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches

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.

Keywords

• Seawater intrusion problem
• sharp-diffuse interface
• existence
• strongly coupled system
• elliptic - degenerate parabolic equations