global attractor
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2022 ◽  
Vol 27 (1) ◽  
pp. 19-37
Author(s):  
Ning Duan ◽  
Xiaopeng Zhao

This paper is concerned with a sixth-order diffusion equation, which describes continuum evolution of film-free surface. By using the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors we verified the existence of global attractor for this surface diffusion equation in the spaces H3(Ω) and fractional-order spaces Hk(Ω), where 0 ≤ k < ∞.


2022 ◽  
pp. 107890
Author(s):  
Yoon Mo Jung ◽  
Bomi Shin ◽  
Sangwoon Yun

2021 ◽  
Vol 38 (1) ◽  
pp. 67-94
Author(s):  
DAVID CHEBAN ◽  

In this paper we give a description of the structure of compact global attractor (Levinson center) for monotone Bohr/Levitan almost periodic dynamical system $x'=f(t,x)$ (*) with the strictly monotone first integral. It is shown that Levinson center of equation (*) consists of the Bohr/Levitan almost periodic (respectively, almost automorphic, recurrent or Poisson stable) solutions. We establish the main results in the framework of general non-autonomous (cocycle) dynamical systems. We also give some applications of theses results to different classes of differential/difference equations.


Author(s):  
Jakub Banaśkiewicz ◽  
Piotr Kalita

AbstractWe study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah–Struwe solutions, which satisfy the Strichartz estimates and coincide with the class of solutions obtained by the Galerkin method. For this class we show the existence and smoothness of pullback, uniform, and cocycle attractors and the relations between them. We also prove that these non-autonomous attractors converge upper-semicontinuously to the global attractor for the limit autonomous problem if the time-dependent nonlinearity tends to a time independent function in an appropriate way.


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