Nonlinear Diffusion Problem Arising in Plasma Physics

1978 ◽  
Vol 40 (26) ◽  
pp. 1720-1722 ◽  
Author(s):  
James G. Berryman ◽  
Charles J. Holland
Keyword(s):  
Plasma Physics ◽  
Nonlinear Diffusion ◽  
Diffusion Problem

Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source

1999 ◽  
Vol 314 (4) ◽  
pp. 703-728 ◽  
Author(s):  
F. Andreu ◽  
J.M. Mazón ◽  
F. Simondon ◽  
J. Toledo
Keyword(s):  
Global Existence ◽  
Nonlinear Diffusion ◽  
Diffusion Problem ◽  
Gradient Term

scholarly journals Free Boundary Determination in Nonlinear Diffusion

2013 ◽  
Vol 3 (4) ◽  
pp. 295-310 ◽  
Author(s):  
M. S. Hussein ◽  
D. Lesnic ◽  
M. Ivanchov
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Nonlinear Diffusion ◽  
Numerical Solutions ◽  
Free Boundary Problems ◽  
Nonlinear Least Squares ◽  
Stability Estimate ◽  
Diffusion Problem ◽  
Boundary Problems ◽  
Minimisation Problem

AbstractFree boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the lsqnonlin routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, instability is manifest in the derivative of the moving free surface, but not in the free surface itself nor in the concentration or temperature.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Youyun Li ◽  
Jinhui Ouyang ◽  
Jiaohua Qin ◽  
Yingli Gao
Keyword(s):  
Nonlinear Problem ◽  
Nonlinear Diffusion ◽  
Diffusion Problem ◽  
Control Model ◽  
Least Square ◽  
Computational Method ◽  
Variable Method ◽  
Linear Diffusion ◽  
Separate Variable ◽  
Diffusion Parameters

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.

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