Existence and uniqueness of radial solutions for fresh/salt water interface equation in a confined aquifer

We prove existence and uniqueness of radial weak solutions of the doubly nonlinear parabolic equationut=div[D(u)ϕ(∇u)],whereD and ϕ satisfy some hypothesis. This cover the particular case where D(s)=s(1-s) and ϕ(p)≔p/(1+|p|2) which is the hydrological case. Numerical simulations are provided also....

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 244; pp. 101 - 117
Main Authors:	Hajj Chehade, H., Jazar, M., Mourad, A.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-10-2014
Subjects:	Comparison principle Nonlinear degenerate Parabolic equations Nonlinear degenerate Parabolic equations Comparison principle
Online Access:	Get full text
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Summary:	We prove existence and uniqueness of radial weak solutions of the doubly nonlinear parabolic equationut=div[D(u)ϕ(∇u)],whereD and ϕ satisfy some hypothesis. This cover the particular case where D(s)=s(1-s) and ϕ(p)≔p/(1+\|p\|2) which is the hydrological case. Numerical simulations are provided also.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2014.06.044