The $\mathbb {H}^{1}$-Compact Global Attractor for Two-Dimensional Convective Brinkman-Forchheimer Equations in Unbounded Domains

2021 ◽  
Author(s):  
Manil T. Mohan
Keyword(s):  
Global Attractor ◽  
Unbounded Domains ◽  
Two Dimensional

scholarly journals Existence of Global Attractors for the Nonlinear Plate Equation with Memory Term

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Lifang Niu ◽  
Jianwen Zhang
Keyword(s):  
Rectangular Plate ◽  
Global Attractor ◽  
Exponential Decay ◽  
Global Attractors ◽  
Memory Term ◽  
Two Dimensional ◽  
Plate Equation ◽  
Memory Kernel ◽  
Nonlinear Plate ◽  
With Memory

A two-dimensional nonlinear plate equation is revisited, which arises from the model of the viscoelastic thin rectangular plate with four edges supported. We establish that the system is exponentially decayed if the memory kernel satisfies the condition of the exponential decay. Furthermore, we show the existence of the global attractor by verifying the condition (C).

scholarly journals Moment Problems on Bounded and Unbounded Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Octav Olteanu
Keyword(s):  
Quadratic Forms ◽  
Necessary Conditions ◽  
Unbounded Domains ◽  
Continuous Functions ◽  
Moment Problems ◽  
Two Dimensional ◽  
Space Of Continuous Functions ◽  
One Dimensional ◽  
Sufficient And Necessary Conditions ◽  
The One

Using approximation results, we characterize the existence of the solution for a two-dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one-dimensional case. For the bounded domain case, one considers a space of complex analytic functions in a disk and a space of continuous functions on a compact interval. The latter result seems to give sufficient (and necessary) conditions for the existence of a multiplicative solution.

Averaging of a nonlinear bipolar model with phase transition and oscillating external forces

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Theodore Tachim Medjo
Keyword(s):  
Phase Transition ◽  
Small Parameter ◽  
Global Attractor ◽  
Bounded Domain ◽  
External Force ◽  
Two Dimensional ◽  
External Forces ◽  
Uniform Global Attractor

AbstractIn this article, we consider a non-autonomous nonlinear bipolar with phase transition in a two-dimensional bounded domain. We assume that the external force is singularly oscillating and depends on a small parameter ϵ. We prove the existence of the uniform global attractor 𝒜

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