Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 764248, 6 pages
http://dx.doi.org/10.1155/2014/764248
Research Article

Lower Bounds Estimate for the Blow-Up Time of a Slow Diffusion Equation with Nonlocal Source and Inner Absorption

School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China

Received 24 July 2013; Accepted 20 December 2013; Published 2 January 2014

Academic Editor: Mufid Abudiab

Copyright © 2014 Zhong Bo Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Springer, New York, NY, USA, 1989. View at MathSciNet
  2. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, NY, USA, 1992. View at MathSciNet
  3. J. Furter and M. Grinfeld, “Local versus non-local interactions in population dynamics,” Journal of Mathematical Biology, vol. 27, no. 1, pp. 65–80, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. H. A. Levine, “Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: the method of unbounded fourier coefficients,” Mathematische Annalen, vol. 214, no. 3, pp. 205–220, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. X. Gao, J. Ding, and B.-Z. Guo, “Blow-up and global solutions for quasilinear parabolic equations with Neumann boundary conditions,” Applicable Analysis, vol. 88, no. 2, pp. 183–191, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. J. Wang, Z. Wang, and J. Yin, “A class of degenerate diffusion equations with mixed boundary conditions,” Journal of Mathematical Analysis and Applications, vol. 298, no. 2, pp. 589–603, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. E. Payne and P. W. Schaefer, “Lower bounds for blow-up time in parabolic problems under Dirichlet conditions,” Journal of Mathematical Analysis and Applications, vol. 328, no. 2, pp. 1196–1205, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. L. E. Payne and J. C. Song, “Lower bounds for blow-up time in a nonlinear parabolic problem,” Journal of Mathematical Analysis and Applications, vol. 354, no. 1, pp. 394–396, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. J. C. Song, “Lower bounds for the blow-up time in a non-local reaction-diffusion problem,” Applied Mathematics Letters, vol. 24, no. 5, pp. 793–796, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. D. Liu, C. Mu, and Q. Xin, “Lower bounds estimate for the blow-up time of a nonlinear nonlocal porous medium equation,” Acta Mathematica Scientia B, vol. 32, no. 3, pp. 1206–1212, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. Z. B. Fang, J. Zhang, and S.-C. Yi, “Roles of weight functions to a nonlocal porous medium equation with inner absorption and nonlocal boundary condition,” Abstract and Applied Analysis, vol. 2012, Article ID 326527, 16 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Talenti, “Best constant in Sobolev inequality,” Annali di Matematica Pura ed Applicata, vol. 110, no. 1, pp. 353–372, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus