A Nonlinear Diffusion Problem with Localized Large Diffusion

2004 ◽  
Vol 29 (5-6) ◽  
pp. 647-670 ◽  
Author(s):  
Noureddine Igbida
Keyword(s):  
Nonlinear Diffusion ◽  
Diffusion Problem ◽  
Large Diffusion

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.

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