Quenching for a nonlinear diffusion equation with a singular boundary condition

1999 ◽  
Vol 50 (4) ◽  
pp. 574 ◽  
Author(s):  
K. Deng ◽  
M. Xu
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Singular Boundary ◽  
Singular Boundary Condition

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 The nonlinear diffusion equation of the ideal barotropic gas through a porous medium

2017 ◽  
Vol 15 (1) ◽  
pp. 895-906
Author(s):  
Huashui Zhan
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Well Posedness ◽  
Initial Value ◽  
Barotropic Gas ◽  
The Ideal

Abstract The nonlinear diffusion equation of the ideal barotropic gas through a porous medium is considered. If the diffusion coefficient is degenerate on the boundary, then the solutions may be controlled by the initial value completely, the well-posedness of the solutions may be obtained without any boundary condition.

Sign in / Sign up

Export Citation Format

Share Document