Blow-up, Life Span and Large Time Behavior of Solutions of a Weakly Coupled System of Reaction-Diffusion Equations

1998 ◽  
pp. 175-197 ◽  
Author(s):  
Kiyoshi Mochizuki
Keyword(s):  
Life Span ◽  
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.

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

scholarly journals Blow-Up Rate Estimates for a System of Reaction-Diffusion Equations with Gradient Terms

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Maan A. Rasheed ◽  
Hassan Abd Salman Al-Dujaly ◽  
Talat Jassim Aldhlki
Keyword(s):  
Blow Up ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Dirichlet Problems ◽  
Blow Up Rate

This paper is concerned with the blow-up properties of Cauchy and Dirichlet problems of a coupled system of Reaction-Diffusion equations with gradient terms. The main goal is to study the influence of the gradient terms on the blow-up profile. Namely, under some conditions on this system, we consider the upper blow-up rate estimates for its blow-up solutions and for the gradients.

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