Numerical investigation of quenching for a nonlinear diffusion equation with a singular Neumann boundary condition

2002 ◽  
Vol 18 (4) ◽  
pp. 429-440 ◽  
Author(s):  
C. I. Christov ◽  
K. Deng
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Numerical Investigation ◽  
Nonlinear Diffusion ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Nonlinear Diffusion Equation

scholarly journals Asymptotic behaviors for nonlocal diffusion equations about the dispersal spread

2020 ◽  
Vol 18 (04) ◽  
pp. 585-614 ◽  
Author(s):  
Yuan-Hang Su ◽  
Wan-Tong Li ◽  
Fei-Ying Yang
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Diffusion Equations ◽  
Nonlocal Diffusion ◽  
Nonlocal Dispersal ◽  
Asymptotic Behaviors ◽  
Cost Parameter ◽  
The Cost

This paper studies the effects of the dispersal spread, which characterizes the dispersal range, on nonlocal diffusion equations with the nonlocal dispersal operator [Formula: see text] and Neumann boundary condition in the spatial heterogeneity environment. More precisely, we are mainly concerned with asymptotic behaviors of generalized principal eigenvalue to the nonlocal dispersal operator, positive stationary solutions and solutions to the nonlocal diffusion KPP equation in both large and small dispersal spread. For large dispersal spread, we show that their asymptotic behaviors are unitary with respect to the cost parameter [Formula: see text]. However, small dispersal spread can lead to different asymptotic behaviors as the cost parameter [Formula: see text] is in a different range. In particular, for the case [Formula: see text], we should point out that asymptotic properties for the nonlocal diffusion equation with Neumann boundary condition are different from those for the nonlocal diffusion equation with Dirichlet boundary condition.

scholarly journals NUMERICAL INVESTIGATION OF THE SHOWALTER - SIDOROV PROBLEM FOR NONLINEAR DIFFUSION EQUATION

2017 ◽  
Vol 21 (10) ◽  
pp. 24-28
Author(s):  
N.A. Manakova ◽  
A.A. Selivanova
Keyword(s):  
Diffusion Equation ◽  
Numerical Investigation ◽  
Nonlinear Diffusion ◽  
Type Equation ◽  
Generalized Solution ◽  
Nonlinear Diffusion Equation ◽  
Sobolev Type ◽  
Equations Of Mathematical Physics ◽  
Sobolev Type Equation ◽  
Vast Area

The article concerns a numerical investigation of nonlinear diffusion mod- el in the circle. Nonlinear diffusion equation simulates the change of potential concentration of viscoelastic fluid, which is filtered in a porous media. This equa- tion is a semilinear Sobolev type equation. Sobolev type equations constitute a vast area of non-classical equations of mathematical physics. Theorem of exis- tence and uniqueness of a weak generalized solution to the Showalter - Sidorov problem for nonlinear diffusion equation is stated. The algorithm of numerical solution to the problem in a circle was developed using the modified Galerkin method. There is a result of computational experiment in this article.

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