A splitting moving mesh method for reaction–diffusion equations of quenching type

2006 ◽  
Vol 215 (2) ◽  
pp. 757-777 ◽  
Author(s):  
Kewei Liang ◽  
Ping Lin ◽  
Ming Tze Ong ◽  
Roger C.E. Tan
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Moving Mesh ◽  
Moving Mesh Method ◽  
Mesh Method

Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System

2016 ◽  
Vol 9 (4) ◽  
pp. 686-704 ◽  
Author(s):  
Congcong Xie ◽  
Xianliang Hu
Keyword(s):  
Finite Element ◽  
Reaction Diffusion ◽  
Equation System ◽  
Reaction Diffusion Equations ◽  
Moving Mesh ◽  
Moving Mesh Method ◽  
Reaction Diffusion Systems ◽  
Pattern Dynamics ◽  
Growing Domain ◽  
Diffusion Systems

AbstractA moving mesh method is proposed for solving reaction-diffusion equations. The finite element method is used to solving the partial different equation system, and an efficient numerical scheme is applied to implement mesh moving. In the practical calculations, the moving mesh step and the problem equation solver are performed alternatively. Several numerical examples are presented, including the Gray-Scott, the Activator-Inhibitor and a case with a growing domain. It is illustrated numerically that the moving mesh methods costs much lower, compared with the numerical schemes on a fixed mesh. Even in the case of complex pattern dynamics described by the reaction-diffusion systems, the adapted meshes can capture the details successfully.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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