Strong global attractor for weakly damped wave equation with sub-quintic nonlinearity

2019 ◽  
Vol 98 ◽  
pp. 314-321
Author(s):  
Cuncai Liu ◽  
Fengjuan Meng ◽  
Chang Zhang
Keyword(s):  
Wave Equation ◽  
Global Attractor ◽  
Damped Wave Equation ◽  
Quintic Nonlinearity

scholarly journals Convergence of Non-autonomous Attractors for Subquintic Weakly Damped Wave Equation

2021 ◽  
Author(s):  
Jakub Banaśkiewicz ◽  
Piotr Kalita
Keyword(s):  
Wave Equation ◽  
Galerkin Method ◽  
Growth Condition ◽  
Global Attractor ◽  
Time Dependent ◽  
Strichartz Estimates ◽  
Damped Wave Equation ◽  
Independent Function ◽  
The Galerkin Method

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.

scholarly journals Strong Global Attractors for 3D Wave Equations with Weakly Damping

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Fengjuan Meng
Keyword(s):  
Wave Equation ◽  
Global Attractor ◽  
Wave Equations ◽  
Global Attractors ◽  
Energy Space ◽  
Damped Wave Equation

We consider the existence of the global attractorA1for the 3D weakly damped wave equation. We prove thatA1is compact in(H2(Ω)∩H01(Ω))×H01(Ω)and attracts all bounded subsets of(H2(Ω)∩H01(Ω))×H01(Ω)with respect to the norm of(H2(Ω)∩H01(Ω))×H01(Ω). Furthermore, this attractor coincides with the global attractor in the weak energy spaceH01(Ω)×L2(Ω).

scholarly journals A note on the global attractor for weakly damped wave equation

2015 ◽  
Vol 41 ◽  
pp. 12-16 ◽  
Author(s):  
Cuncai Liu ◽  
Fengjuan Meng ◽  
Chengkui Zhong
Keyword(s):  
Wave Equation ◽  
Global Attractor ◽  
Damped Wave Equation
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