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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 796812, 8 pages
Research Article

An Optimal Method for Diffusion Parameters of Nonlinear Diffusion Problem of Drug Releasing in 2D-Disc Device by Separate Variable Method

1State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Beijing 100038, China
2College of Highway Engineering, Changsha University of Science and Technology, Hunan, 410004, China
3College of Computer, Central South University of Forestry and Technology, Changsha 410004, China

Received 14 November 2013; Revised 16 February 2014; Accepted 16 February 2014; Published 23 March 2014

Academic Editor: Vassilios C. Loukopoulos

Copyright © 2014 Youyun Li 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.


An optimization control model and the corresponding computational method drawing the diffusion parameters of the nonlinear problem for the drug releasing in the 2D-disc device were given in this paper. Firstly, based on the nonlinear diffusion equation of the drug releasing in the 2D-disc device, we used the linear diffusion problem to discrete the nonlinear diffusion problem with the discrete space and the discrete time. Then, by the separate variable method, the solution of the linear problem was given. Next, the least square method based on the separate variable idea (LSMSV) was used to estimate the nonlinear appropriate diffusion parameters. Finally, a numerical example was presented to show that the control model and the numerical method were valid for computing the diffusion coefficient of the nonlinear problem for the drug releasing in the 2D-disc device.