scholarly journals Pullback Attractors for Nonautonomous Degenerate Kirchhoff Equations with Strong Damping

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Honglv Ma ◽  
Jing Wang ◽  
Jun Xie
Keyword(s):  
Measure Of Noncompactness ◽  
Stiffness Coefficient ◽  
Pullback Attractors ◽  
Kirchhoff Equations ◽  
Strong Damping

In this paper, we obtain the existence of pullback attractors for nonautonomous Kirchhoff equations with strong damping, which covers the case of possible generation of the stiffness coefficient. For this purpose, a necessary method via “the measure of noncompactness” is established.

The Pullback Asymptotic Behavior of the Solutions for 2D NonautonomousG-Navier-Stokes Equations

2012 ◽  
Vol 4 (2) ◽  
pp. 223-237 ◽  
Author(s):  
Jinping Jiang ◽  
Yanren Hou ◽  
Xiaoxia Wang
Keyword(s):  
Asymptotic Behavior ◽  
Measure Of Noncompactness ◽  
Dirichlet Boundary ◽  
Stokes Equations ◽  
Fractal Dimensions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Pullback Attractors ◽  
Navier Stokes Equations

AbstractThe pullback asymptotic behavior of the solutions for 2D Nonau-tonomousG-Navier-Stokes equations is studied, and the existence of itsL2-pullback attractors on some bounded domains with Dirichlet boundary conditions is investigated by using the measure of noncompactness. Then the estimation of the fractal dimensions for the 2DG-Navier-Stokes equations is given.

scholarly journals Kirchhoff equations with strong damping

2016 ◽  
Vol 16 (2) ◽  
pp. 441-482 ◽  
Author(s):  
Marina Ghisi ◽  
Massimo Gobbino
Keyword(s):  
Kirchhoff Equations ◽  
Strong Damping

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

Numerical and Experimental Research on the Fluid-Induced Forces of Clearance Flow in Canned Motor Reactor Coolant Pump

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Rui Xu ◽  
Yun Long ◽  
Yaoyu Hu ◽  
Junlian Yin ◽  
Dezhong Wang
Keyword(s):  
Large Mass ◽  
Stiffness Coefficient ◽  
Pressurized Water ◽  
Coolant Pump ◽  
Reactor Coolant ◽  
Various Boundary Conditions ◽  
Clearance Flow ◽  
Mass Coefficient ◽  
Cfd Method ◽  
Canned Motor

Reactor coolant pump (RCP) is one of the most important equipment of the coolant loop in a pressurized water reactor system. Its safety relies on the characteristics of the rotordynamic system. For a canned motor RCP, the liquid coolant fills up the clearance between the metal shields of the rotor and stator inside the canned motor, forming a long clearance flow. The fluid-induced forces of the clearance flow in canned motor RCP and their effects on the rotordynamic characteristics of the pump are numerically and experimentally analyzed in this work. A transient computational fluid dynamics (CFD) method has been used to investigate the fluid-induced force of the clearance. A vertical experiment rig has also been established for the purpose of measuring the fluid-induced forces. Fluid-induced forces of clearance flow with various whirl frequencies and various boundary conditions are obtained through the CFD method and the experiment. Results show that clearance flow brings large mass coefficient into the rotordynamic system and the direct stiffness coefficient is negative under the normal operating condition. The rotordynamic stability of canned motor RCP does not deteriorate despite the existence of significant cross-coupled stiffness coefficient from the fluid-induced forces of the clearance flow.

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