scholarly journals Finite dimensionality of global attractors for a non-classical reaction–diffusion equation with memory

2012 ◽  
Vol 25 (3) ◽  
pp. 357-362 ◽  
Author(s):  
Tao Chen ◽  
Zhe Chen ◽  
Yanbin Tang
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equation ◽  
Finite Dimensionality ◽  
With Memory

scholarly journals A reaction-diffusion equation on a thin L-shaped domain

1995 ◽  
Vol 125 (2) ◽  
pp. 283-327 ◽  
Author(s):  
Jack K. Hale ◽  
Geneviève Raugel
Keyword(s):  
Diffusion Equation ◽  
Lower Semicontinuity ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equation ◽  
Limit Equation ◽  
One Dimensional ◽  
Shaped Domain

We consider a dissipative reaction–diffusion equation on a thin L-shaped domain (with the thinness measured by a parameter ε); we determine the limit equation for ε = 0 and prove the upper semicontinuity of the global attractors at ε = 0. We also state a lower semicontinuity result. When the limit equation is one-dimensional, we prove convergence of any orbit to a singleton.

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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