About this Journal Submit a Manuscript Table of Contents 
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 326527, 16 pages
doi:10.1155/2012/326527
Research Article

Roles of Weight Functions to a Nonlocal Porous Medium Equation with Inner Absorption and Nonlocal Boundary Condition

Zhong Bo Fang,1 Jianyun Zhang,1 and Su-Cheol Yi2

1School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
2Department of Mathematics, Changwon National University, Changwon 641-773, Republic of Korea

Received 22 August 2012; Revised 24 October 2012; Accepted 7 November 2012

Academic Editor: Dragoş-Pătru Covei

Copyright © 2012 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, vol. 83 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989. View at Zentralblatt MATH
  2. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, NY, USA, 1992. View at Zentralblatt MATH
  3. J. Furter and M. Grinfeld, “Local versus nonlocal interactions in population dynamics,” Journal of Mathematical Biology, vol. 27, no. 1, pp. 65–80, 1989. View at Publisher · View at Google Scholar
  4. \. Calsina, C. Perelló, and J. Saldaña, “Non-local reaction-diffusion equations modelling predator-prey coevolution,” Publicacions Matemàtiques, vol. 38, no. 2, pp. 315–325, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. W. Allegretto, G. Fragnelli, P. Nistri, and D. Papini, “Coexistence and optimal control problems for a degenerate predator-prey model,” Journal of Mathematical Analysis and Applications, vol. 378, no. 2, pp. 528–540, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. W. A. Day, “Extensions of a property of the heat equation to linear thermoelasticity and other theories,” Quarterly of Applied Mathematics, vol. 40, no. 3, pp. 319–330, 1982/83.
  7. W. A. Day, “A decreasing property of solutions of parabolic equations with applications to thermoelasticity,” Quarterly of Applied Mathematics, vol. 40, no. 4, pp. 468–475, 1982/83.
  8. A. Friedman, “Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions,” Quarterly of Applied Mathematics, vol. 44, no. 3, pp. 401–407, 1986. View at Zentralblatt MATH
  9. C. V. Pao, “Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions,” Journal of Computational and Applied Mathematics, vol. 88, no. 1, pp. 225–238, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Y. L. Wang, C. L. Mu, and Z. Y. Xiang, “Blowup of solutions to a porous medium equation with nonlocal boundary condition,” Applied Mathematics and Computation, vol. 192, no. 2, pp. 579–585, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Z. G. Lin and Y. R. Liu, “Uniform blowup profiles for diffusion equations with nonlocal source and nonlocal boundary,” Acta Mathematica Scientia, Series B, vol. 24, no. 3, pp. 443–450, 2004.
  12. Z. J. Cui and Z. D. Yang, “Roles of weight functions to a nonlinear porous medium equation with nonlocal source and nonlocal boundary condition,” Journal of Mathematical Analysis and Applications, vol. 342, no. 1, pp. 559–570, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. N. Zheng and L. H. Kong, “Roles of weight functions in a nonlinear nonlocal parabolic system,” Nonlinear Analysis, vol. 68, no. 8, pp. 2406–2416, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Y. L. Wang, C. L. Mu, and Z. Y. Xiang, “Properties of positive solution for nonlocal reaction diffusion equation with nonlocal boundary,” Boundary Value Problems, vol. 2007, Article ID 064579, 12 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. C. L. Mu, D. M. Liu, and S. M. Zhou, “Properties of positive solutions for a nonlocal reaction-diffusion equation with nonlocal nonlinear boundary condition,” Journal of the Korean Mathematical Society, vol. 47, no. 6, pp. 1317–1328, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. M. X. Wang and Y. Wang, “Properties of positive solutions for non-local reaction-diffusion problems,” Mathematical Methods in the Applied Sciences, vol. 19, no. 14, pp. 1141–1156, 1996. View at Publisher · View at Google Scholar
  17. J. R. Anderson, “Local existence and uniqueness of solutions of degenerate parabolic equations,” Communications in Partial Differential Equations, vol. 16, no. 1, pp. 105–143, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. Y. F. Yin, “On nonlinear parabolic equations with nonlocal boundary condition,” Journal of Mathematical Analysis and Applications, vol. 185, no. 1, pp. 161–174, 1994. View at Publisher · View at Google Scholar
  19. L. Damascelli, “Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results,” Annales de l'Institut Henri Poincaré, vol. 15, no. 4, pp. 493–516, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. F. C. Li, “Global existence and blow-up of solutions to a nonlocal quasilinear degenerate parabolic system,” Nonlinear Analysis, vol. 67, no. 5, pp. 1387–1402, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH