Share This Article:

The Role of Space Dimension on the Blow up for a Reaction-Diffusion Equation

Abstract Full-Text HTML Download Download as PDF (Size:77KB) PP. 575-578
DOI: 10.4236/am.2011.25076    5,423 Downloads   8,772 Views   Citations
Author(s)    Leave a comment

ABSTRACT

This paper deals with the doubly degenerate reaction-di?usion equation where , , and B(0,1) denotes a unit ball in RN with the center in origin. We prove that the blow up phenomenon can be restrained if the space dimension N is taken su?ciently large. Moreover, the critical condition guaranteeing the absence (or occurrence) of the blow up is achieved.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Z. Liang, "The Role of Space Dimension on the Blow up for a Reaction-Diffusion Equation," Applied Mathematics, Vol. 2 No. 5, 2011, pp. 575-578. doi: 10.4236/am.2011.25076.

References

[1] Z. L. Liang, “Blow up Rate for a Porous Medium Equation with Power Nonlinearity,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, No. 11, 2010, pp. 3507-3512. doi:10.1016/j.na.2010.06.078
[2] A. Samarskii, V. Galaktionov and V. Kurdyumov, “Blow up in Quasilinear Parabolic Equations,” Walter de Gruyter, Berlin, 1995.
[3] A. Tersenov, “Space Dimension Can Prevent the Blowup of Solution for Parabolic Problems,” Electronic Journal of Differential Equations Vol. 165, No. 165, 2007, pp. 1- 6.
[4] J. N. Zhao, “Existence and Nonexistence of Solutions for ,” Journal of Mathe- matical Analysis and Applications, Vol. 172, No. 1, 1993, pp. 130-146. doi:10.1006/jmaa.1993.1012
[5] D. Andreucci and A. F. Tedeev, “Universal Bounds at the Blow-Up Time for Nonlinear Parabolic Equation,” Advances in Differential Equations, Vol. 10, No. 1, 2005, pp. 89-120.
[6] Z. Q. Wu, J. N. Zhao and J. X. Yin, et al., “Nonlinear Diffusion Equations,” World Scientific Publishing Co., Inc., River Edge, 2001.
[7] Z. L. Liang and J. N. Zhao, “Localization for the Evolution p-Laplacian Equation with Strongly Nonlinear Source Term,” Journal of Differential Equations, Vol. 246, No. 1, 2009, pp. 391-407. doi:10.1016/j.jde.2008.07.038

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.