Upper semicontinuity of Nemytskij operators

1991 ◽  
Vol 160 (1) ◽  
pp. 321-330 ◽  
Author(s):  
A. Cellina ◽  
A. Fryszkowski ◽  
T. Rzezuchowski
2005 ◽  
Vol 2005 (3) ◽  
pp. 273-288 ◽  
Author(s):  
Ahmed Y. Abdallah

We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert spacel2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.


Author(s):  
Panpan Zhang ◽  
Anhui Gu

This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.


2008 ◽  
Vol 18 (03) ◽  
pp. 695-716 ◽  
Author(s):  
BIXIANG WANG

We study the asymptotic behavior of nonautonomous discrete Reaction–Diffusion systems defined on multidimensional infinite lattices. We show that the nonautonomous systems possess uniform attractors which attract all solutions uniformly with respect to the translations of external terms when time goes to infinity. These attractors are compact subsets of weighted spaces, and contain all bounded solutions of the system. The upper semicontinuity of the uniform attractors is established when an infinite-dimensional reaction–diffusion system is approached by a family of finite-dimensional systems. We also examine the limiting behavior of lattice systems with almost periodic, rapidly oscillating external terms in weighted spaces. In this case, it is proved that the uniform global attractors of nonautonomous systems converge to the global attractor of an averaged autonomous system.


2015 ◽  
Vol 128 ◽  
pp. 303-324 ◽  
Author(s):  
Hongyong Cui ◽  
Yangrong Li ◽  
Jinyan Yin

1989 ◽  
Vol 65 ◽  
pp. 161
Author(s):  
L. A. Tarrio ◽  
A. G. Rodicio
Keyword(s):  

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