scholarly journals Long-Time Behavior of a Reaction–Diffusion Model with Strong Allee Effect and Free Boundary: Effect of Protection Zone

2021 ◽  
Author(s):  
Ningkui Sun ◽  
Chengxia Lei
Keyword(s):  
Free Boundary ◽  
Allee Effect ◽  
Boundary Effect ◽  
Reaction Diffusion ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Protection Zone ◽  
Reaction Diffusion Model ◽  
Long Time ◽  
Strong Allee Effect

Long-time behavior of solutions and chaos in reaction-diffusion equations

2017 ◽  
Vol 99 ◽  
pp. 91-100 ◽  
Author(s):  
Kamal N. Soltanov ◽  
Anatolij K. Prykarpatski ◽  
Denis Blackmore
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

LONG-TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR REACTION DIFFUSION EQUATIONS INVOLVING L1 DATA

2012 ◽  
Vol 14 (01) ◽  
pp. 1250007 ◽  
Author(s):  
CHENGKUI ZHONG ◽  
WEISHENG NIU
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Smooth Bounded Domain ◽  
Bootstrap Argument ◽  
Nonlinear Reaction ◽  
L1 Data ◽  
Long Time

In this paper we consider the long-time behavior of solutions to nonlinear reaction diffusion equations involving L1 data, [Formula: see text] where Ω is a smooth bounded domain and u0, g ∈ L1(Ω). Using a decomposition technique combined with a bootstrap argument we establish some uniform regularity results on the solutions, by which we prove that the solution semigroup generated by the problem above possesses a global attractor [Formula: see text] in L1(Ω). Moreover, we obtain that the attractor is actually invariant, compact in [Formula: see text], q < max {N/(N-1), (2p-2)/p}, and attracts every bounded subset of L1(Ω) in the norm of [Formula: see text], 1 ≤ r < ∞.

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