- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 326527, 16 pages
Roles of Weight Functions to a Nonlocal Porous Medium Equation with Inner Absorption and Nonlocal Boundary Condition
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.
- J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, vol. 83 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989.
- C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, NY, USA, 1992.
- J. Furter and M. Grinfeld, “Local versus nonlocal interactions in population dynamics,” Journal of Mathematical Biology, vol. 27, no. 1, pp. 65–80, 1989.
- \. 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.