Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 2
Submit an article Journal homepage
155
Views
1
CrossRef citations to date
0
Altmetric
Articles

Blow-up rate for the heat equation with a memory boundary condition

Keng DengDepartment of Mathematics, University of Louisiana at Lafayette, Lafayette, LA70504, USA.Correspondence[email protected]
&
Qian WangDepartment of Mathematics, University of Louisiana at Lafayette, Lafayette, LA70504, USA.
Pages 308-317 | Received 26 Nov 2013, Accepted 03 Feb 2014, Published online: 14 Mar 2014

References

  • Levine HA, Pamuk S, Sleeman B, Nilsen-Hamilton M. Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull. Math. Biol. 2001;63:801–863.
  • Ciarletta M. A differential problem for heat equation with a boundary condition with memory. Appl. Math. Lett. 1997;10:95–101.
  • Fabrizio M, Morro A. Mathematical problems in linear viscoelasticity. Vol. 12, SIAM studies in applied mathematics. Philadelphia (PA): SIAM; 1992.
  • Gurtin ME, Pipkin AP. A general theory of heat conduction with finite wave speeds. Arch. Rational Mech. Anal. 1968;31:113–126.
  • Fabrizio M, Morro A. A boundary condition with memory in electromagnetism. Arch. Rational Mech. Anal. 1996;136:359–381.
  • López-Gómez J, Márquez V, Wolanski N. Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition. J. Differ. Equ. 1991;92:384–401.
  • Rial DF, Rossi JD. Blow-up results and localization of blow-up points in an N-dimensional smooth domain. Duke Math. J. 1997;88:391–405.
  • 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.
  • Deng K. The blow-up behavior of the heat equation with Neumann boundary conditions. J. Math. Anal. Appl. 1994;188:641–650.
  • Anderson JR, Deng K, Dong Z. Global solvability for the heat equation with boundary flux governed by nonlinear memory. Quart. Appl. Math. 2011;69:759–770.
  • Hu B, Yin H-M. Critical exponents for a system of heat equations coupled in a non-linear boundary condition. Math. Methods Appl. Sci. 1996;19:1099–1120.
  • Hu B, Yin H-M. The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition. Trans. Amer. Math. Soc. 1994;346:117–135.
  • Friedman A. Partial differential equations of parabolic type. Englewood Cliffs (NJ): Prentice-Hall; 1964.
  • Fila M, Quittner P. The blow-up rate for the heat equation with a nonlinear boundary condition. Math. Methods Appl. Sci. 1991;14:197–205.
  • Amann H. Parabolic equations and nonlinear boundary conditions. J. Differ. Equ. 1988;72:201–269.
  • Garroni MG, Menaldi JL. Green functions for second order parabolic integro-differential problems. New York (NY): Longman Scientific and Technical; 1992.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.