scholarly journals Pullback attractors for non-autonomous reaction–diffusion equation with infinite delays in C γ , L r ( Ω ) $C_{\gamma,L^{r}(\Omega)}$ or C γ , W 1 , r ( Ω ) $C_{\gamma,W^{1,r}(\Omega)}$

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Yanping Ran ◽  
Jing Li
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Pullback Attractors ◽  
Infinite Delays

Pullback Attractors for a Reaction–Diffusion Equation in a General Nonempty Open Subset of ℝN with Nonautonomous Forcing Term in H−1

2015 ◽  
Vol 25 (12) ◽  
pp. 1550164
Author(s):  
María Anguiano
Keyword(s):  
Diffusion Equation ◽  
Growth Condition ◽  
Open Subset ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Nonempty Open Subset ◽  
Pullback Attractors ◽  
Main Concept ◽  
Asymptotic Compactness ◽  
Bounded Sets

The existence of minimal pullback attractors in [Formula: see text] for a nonautonomous reaction–diffusion equation, in the frameworks of universes of fixed bounded sets and that given by a tempered growth condition, is proved in this paper, when the domain [Formula: see text] is a general nonempty open subset of [Formula: see text], and [Formula: see text]. The main concept used in the proof is the asymptotic compactness of the process generated by the problem. The relation among these families is also discussed.

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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