scholarly journals On Conditions for the Stability of a Two Component Mixed Quasimonotone Reaction Diffusion Equation

2001 ◽  
Vol 256 (2) ◽  
pp. 513-524
Author(s):  
E.A. Gaffney
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Component ◽  
The Stability

scholarly journals About the Structure of Attractors for a Nonlocal Chafee-Infante Problem

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 353
Author(s):  
Rubén Caballero ◽  
Alexandre N. Carvalho ◽  
Pedro Marín-Rubio ◽  
José Valero
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Fixed Points ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Stationary Points ◽  
The Cauchy Problem ◽  
The Stability ◽  
Nonlocal Reaction ◽  
Multivalued Semiflow

In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing that the problem undergoes the same cascade of bifurcations as in the Chafee-Infante equation. Second, we study the stability of the fixed points and establish that the semiflow is a dynamic gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections.

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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