Publication Cover
Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 5
95
Views
3
CrossRef citations to date
0
Altmetric
Articles

A fast diffusion model with memory at the boundary: global solvability in the critical case

Pages 771-777 | Received 29 Dec 2015, Accepted 19 Feb 2016, Published online: 13 Mar 2016

References

  • Deng K, Wang Q. Global existence and blow-up for the fast diffusion equation with a memory boundary condition. Q. Appl. Math. Forthcoming, http://dx.doi.org/10.1090/qam/1425.
  • Anderson J, Deng K, Wang Q. Global behavior of solutions to the fast diffusion equation with boundary flux governed by memory Math. Methods Appl. Sci. 2016, doi: 10.1002/mma.3874.
  • Anderson J, Deng K. Global solvability for the porous medium equation with boundary flux governed by nonlinear memory. J. Math. Anal. Appl. 2015;423:1183–1202.
  • Anderson J, Deng K, Dong Z. Global Solvability for the heat equation with boundary flux governed by nonlinear memory. Q. Appl. Math. 2011;69:759–770.
  • Anderson J. Local existence and uniqueness of solutions of degenerate parabolic equations. Commun. Partial Differ. Equ. 1991;16:105–143.
  • Sacks P. Continuity of solutions of a singular parabolic equation. Nonlinear Anal. 1983;7:387–409.
  • Levine H, Pamuk S, Sleeman B, et al. Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull. Math. Biol. 2001;63:801–863.
  • Walter W. On existence and nonexistence in the large of solutions of parabolic differential equations with a nonlinear boundary condition. SIAM J. Math. Anal. 1975;6:85–90.
  • Filo J. Diffusivity versus absorption through the boundary. J. Differ. Equ. 1992;99:281–305.
  • Wu YH. Existence and behavior of solutions of nonlinear evolution equations [ Doctoral dissertation]. Institute of Systems Science, Chinese Academy of Sciences, Beijing;1993.
  • Wang MX, Wu YH. Global existence and blow up problems for quasilinear parabolic equations with nonlinear boundary conditions. SIAM J. Math. Anal. 1993;24:1515–1521.
  • Wolanski N. Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary. SIAM J. Math. Anal. 1993;24:317–326.
  • Wang MX. The long-time behavior of solutions to a class of quasilinear parabolic equations with nonlinear boundary conditions. Acta Math. Sin. 1996;39:118–124.

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.