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- W4301868420 abstract "We study the large time behavior of the solutions to a two phase extension of the porous medium equation, which models the so-called seawater intrusion problem. The goal is to identify the self-similar solutions that correspond to steady states of a rescaled version of the problem. We fully characterize the unique steady states that are identified as minimizers of a convex energy and shown to be radially symmetric. Moreover, we prove the convergence of the solution to the time-dependent model towards the unique stationary state as time goes to infinity. We finally provide numerical illustrations of the stationary states and we exhibit numerical convergence rates." @default.
- W4301868420 created "2022-10-05" @default.
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- W4301868420 date "2018-03-28" @default.
- W4301868420 modified "2023-09-30" @default.
- W4301868420 title "Large time behavior of a two phase extension of the porous medium equation" @default.
- W4301868420 doi "https://doi.org/10.48550/arxiv.1803.10476" @default.
- W4301868420 hasPublicationYear "2018" @default.
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