scholarly journals Existence of strong solutions and global attractors for the coupled suspension bridge equations

2009 ◽  
Vol 246 (10) ◽  
pp. 3755-3775 ◽  
Author(s):  
Qiaozhen Ma ◽  
Chengkui Zhong
Keyword(s):  
Strong Solutions ◽  
Suspension Bridge ◽  
Global Attractors

Existence of strong solutions and global attractors for the suspension bridge equations

2007 ◽  
Vol 67 (2) ◽  
pp. 442-454 ◽  
Author(s):  
Chengkui Zhong ◽  
Qiaozhen Ma ◽  
Chunyou Sun
Keyword(s):  
Strong Solutions ◽  
Suspension Bridge ◽  
Global Attractors

scholarly journals Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Xuan Wang ◽  
Qiaozhen Ma
Keyword(s):  
Hilbert Space ◽  
Dynamical Behavior ◽  
Type Equation ◽  
Strong Solutions ◽  
Suspension Bridge ◽  
Bridge Type ◽  
Uniform Attractors ◽  
External Forces ◽  
Higher Regularity

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert spaceD(A)×H2(Ω)∩H01(Ω), where the nonlinearityg(u,t)is translation compact and the time-dependent external forcesh(x,t)only satisfy condition (C*) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.

scholarly journals Strong Solutions and Global Attractors for Kirchhoff Type Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xiangping Chen
Keyword(s):  
Phase Space ◽  
Type Equation ◽  
Strong Solutions ◽  
Global Attractors ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Long Time ◽  
Linear Damping

We study the long-time behavior of the Kirchhoff type equation with linear damping. We prove the existence of strong solution and the semigroup associated with the solution possesses a global attractor in the higher phase space.

scholarly journals On Lr-regularity of global attractors generated by strong solutions of reaction-diffusion equations

2016 ◽  
Vol 1 (2) ◽  
pp. 375-390 ◽  
Author(s):  
José Valero
Keyword(s):  
Nonlinear Term ◽  
Mild Solutions ◽  
Reaction Diffusion ◽  
Strong Solutions ◽  
Global Attractors ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
The Cauchy Problem ◽  
Weak Attractor

AbstractIn this paper we prove that the global attractor generated by strong solutions of a reaction-diffusion equation without uniqueness of the Cauchy problem is bounded in suitable Lr-spaces. In order to obtain this result we prove first that the concepts of weak and mild solutions are equivalent under an appropriate assumption.Also, when the nonlinear term of the equation satisfies a supercritical growth condition the existence of a weak attractor is established.

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