52
Views
0
CrossRef citations to date
0
Altmetric
Articles

The asymptotic properties of solutions to a multi-dimensional Newtonian filtration equations

&
Pages 1749-1766 | Received 19 Aug 2016, Accepted 22 Mar 2017, Published online: 03 Apr 2017

References

  • Kalashnikov AS. Some problems of the qualitative theory of nonlinear degenerate parabolic equations of second order. Russ Math Surv. 1987;44(2):169–222.
  • Wu ZQ, Zhao JN, Yin JX, et al. Nonlinear diffusion equations. River Edge (NJ): World Scientific; 2001.
  • Dibenedetto E. Degenerate parabolic equations. Berlin: Springer-Verlag; 1993.
  • Galaktionov VA, Levine HA. On the critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary. Israel J Math. 1996;94(1):125–146.
  • Quirós F, Rossi JD. Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions. Indiana Univ Math J. 2001;50(1):629–654.
  • Zheng SN, Song XF, Jiang ZX. Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux. J Math Anal Appl. 2004;298:308–324.
  • Wang ZJ, Yin JX, Wang CP, et al. Large time behavior of solutions to Newtonian equation with nonlinear boundary sources. J Evol Equ. 2007;7:615–648.
  • Wang ZJ, Zhou Q, Lou WQ. Critical exponents for porous medium system coupled via nonlinear boundary flux. Nonlinear Anal. 2009;71:2134–2140.
  • Ling ZQ. Critical curves and non-extinction conditions for a 2-dimensional non-Newtonian polytropic filtration equations coupled via nonlinear boundary flux. J Appl Math Comput. 2016;51:53–66.
  • Hu B, Yin HM. On critical exponents for the heat equation with a nonlinear boundary condition. Ann Inst H Poincaré Anal Non-Linéaire. 1996;13(6):707–732.
  • Anderson JR. Local existence and uniqueness of solutions of degenerate parabolic equations. Commun Partial Differ Equ. 1991;16:105–143.

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.