scholarly journals Blow-up and Large Time Behavior of Solutions of a Weakly Coupled System of Reaction-Diffusion Equations

2003 ◽  
Vol 27 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Noriaki Umeda
Keyword(s):  
Large Time ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Time Behavior ◽  
Weakly Coupled ◽  
Weakly Coupled System

A FEM FOR A SYSTEM OF SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS SOURCE TERM

2013 ◽  
Vol 10 (05) ◽  
pp. 1350057
Author(s):  
A. RAMESH BABU ◽  
N. RAMANUJAM
Keyword(s):  
Reaction Diffusion ◽  
Coupled System ◽  
Perturbation Parameter ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Shishkin Meshes ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Discontinuous Source Term ◽  
Interior Layers

In this paper, we consider a weakly coupled system of two reaction-diffusion equations with discontinuous source terms. When a parameter multiplying the second order derivatives in the equations is small, their solutions exhibit boundary layers as well as interior layers. A numerical method based on finite element and Shishkin and Bakhvalov–Shishkin meshes is presented. We derive an error estimate of order O(N-1ln N) in the energy norm with respect to the perturbation parameter. Numerical experiments are also presented to support our theoritical results.

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