Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 10
78
Views
2
CrossRef citations to date
0
Altmetric
Articles

Global weak solutions for a degenerate parabolic system modelling seawater intrusion in confined aquifers

, &
Pages 1749-1764 | Received 05 Sep 2018, Accepted 01 Nov 2018, Published online: 15 Nov 2018

References

  • Jazar M, Monneau R. Derivation of seawater intrusion models by formal asymptotics. SIAM J Appl Math. 2014;74(4):1152–1173. doi: 10.1137/120867561
  • Alkhayal J, Monneau R, Jazar M, et al. Existence result for degenerate cross-diffusion systems with application to seawater intrusion. ESAIM: Control, Optimization and Calculus of Variations. 2017.
  • Chen L, Jüngel A. Analysis of a multidimensional parabolic population model with strong cross-diffusion. SIAM J Math Anal. 2004;36(1):301–322. doi: 10.1137/S0036141003427798
  • Chen L, Jüngel A. Analysis of a parabolic cross-diffusion population model without self-diffusion. J Differ Equ. 2006;224(1):39–59. doi: 10.1016/j.jde.2005.08.002
  • Laurençot P, Matioc B-V. A gradient flow approach to a thin film approximation of the muskat problem. Calc Var Partial Differ Equ. 2013;47(1–2):319–341. doi: 10.1007/s00526-012-0520-5
  • Matioc B-V. Non-negative global weak solutions for a degenerate parabolic system modelling thin films driven by capillarity. Proc R Soc Edinb. 2012;142(05):1071–1085. doi: 10.1017/S0308210511000680
  • Wen Z, Fu S. Global solutions to a class of multi-species reaction-diffusion systems with cross-diffusions arising in population dynamics. J Comput Appl Math. 2009;230(1):34–43. doi: 10.1016/j.cam.2008.10.064
  • Wilhelm Alt H, Luckhaus S. Quasilinear elliptic-parabolic differential equations. Math Z. 1983;183(3):311–341. doi: 10.1007/BF01176474
  • Choquet C, Li J, Rosier C. Global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches. Electronic J Differ Equ. 2015;2015(126):1–27.
  • Najib K, Rosier C. On the global existence for a degenerate elliptic–parabolic seawater intrusion problem. Math Comput Simul. 2011;81(10):2282–2295. doi: 10.1016/j.matcom.2010.12.026
  • Talibi MEA, Tber MH. Existence of solutions for a degenerate seawater intrusion problem. Electron J Differ Equ. 2005;2005(72):1–14.
  • Evans LC. Partial differential equations. Providence, RI: American Mathematical Society; 1998. (Graduate studies in mathematics; 19).
  • Lions J-L, Magenes E. Problemes aux limites non homogenes, Vol. 1. Paris: Dunod; 1968.
  • Simon J. Compact sets in the space Lp(0,T;B). Ann Mat Pura Appl. 1986;146(1):65–96. doi: 10.1007/BF01762360

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.