Exponential attractors for reaction–diffusion equations with arbitrary polynomial growth

2009 ◽  
Vol 71 (3-4) ◽  
pp. 751-765 ◽  
Author(s):  
Yansheng Zhong ◽  
Chengkui Zhong
Keyword(s):  
Polynomial Growth ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Exponential Attractors ◽  
Arbitrary Polynomial

Pullback Exponential Attractors for Nonautonomous Reaction–Diffusion Equations

2015 ◽  
Vol 25 (05) ◽  
pp. 1550063
Author(s):  
Xingjie Yan ◽  
Wei Qi
Keyword(s):  
A Priori ◽  
Reaction Diffusion ◽  
A Priori Estimate ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Exponential Attractor ◽  
Exponential Attractors ◽  
Estimate Method ◽  
Necessary And Sufficient ◽  
Asymptotic A Priori Estimate

This paper presents a necessary and sufficient condition to prove the existence of the pullback exponential attractor. The asymptotic a priori estimate method is used to produce an abstract result on the existence of the pullback exponential attractor in a strong space without regularity. The established results are illustrated by applying them to the nonautonomous reaction–diffusion equations to prove the existence of the pullback exponential attractors in L2(Ω), [Formula: see text] and Lp(Ω)(p > 2) spaces.

scholarly journals On Nonlinear Nonlocal Systems of Reaction Diffusion Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
B. Ahmad ◽  
M. S. Alhothuali ◽  
H. H. Alsulami ◽  
M. Kirane ◽  
S. Timoshin
Keyword(s):  
Growth Condition ◽  
Anomalous Diffusion ◽  
Polynomial Growth ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion System ◽  
Diffusion Equations ◽  
Reaction Term ◽  
Polynomial Growth Condition

The reaction diffusion system with anomalous diffusion and a balance lawut+-Δα/2u=-fu,v,   vt+-∆β/2v=fu,v,0<α,β<2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction termfwhen0<α≤β≤2; (ii) no growth condition is imposed on the reaction termfwhen0<β≤α≤2.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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