NUMERICAL QUENCHING FOR A NON-NEWTONIAN FILTRATION EQUATION WITH SINGULAR BOUNDARY FLUX

2021 ◽  
Vol 10 (4) ◽  
pp. 1879-1898
Author(s):  
G. M. Camara ◽  
K. N’Guessan ◽  
A. Coulibaly ◽  
A. K. Toure
Keyword(s):  
Singular Boundary ◽  
Filtration Equation ◽  
Boundary Flux ◽  
Singular Boundary Flux

NUMERICAL QUENCHING FOR A NONLINEAR DIFFUSION EQUATION WITH SINGULAR BOUNDARY FLUX

2021 ◽  
Vol 10 (12) ◽  
pp. 3649-3667
Author(s):  
A.R. Anoh ◽  
K. N’Guessan ◽  
A. Coulibaly ◽  
A.K. Toure
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Numerical Experiments ◽  
Mesh Size ◽  
Nonlinear Diffusion Equation ◽  
Singular Boundary ◽  
Semidiscrete Approximation ◽  
Boundary Flux ◽  
Quenching Time ◽  
Singular Boundary Flux

In this paper, we study the semidiscrete approximation of the solution of a nonlinear diffusion equation with nonlinear source and singular boundary flux. We find some conditions under which the solution of the semidiscrete form quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis.

scholarly journals Quenching for a Non-Newtonian Filtration Equation with a Singular Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Xiliu Li ◽  
Chunlai Mu ◽  
Qingna Zhang ◽  
Shouming Zhou
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Time ◽  
Singular Boundary ◽  
Quenching Rate ◽  
Filtration Equation ◽  
Laplacian Equation ◽  
Singular Boundary Condition

This paper deals with a nonlinearp-Laplacian equation with singular boundary conditions. Under proper conditions, the solution of this equation quenches in finite time and the only quenching point thatisx=1are obtained. Moreover, the quenching rate of this equation is established. Finally, we give an example of an application of our results.

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