On global attractors for a nonlinear porous elastic system with fractional power in the memory term

2021 ◽  
pp. 20
Author(s):  
Mirelson Martins Freitas ◽  
Anderson J. A. Ramos ◽  
Mauro L. Santos ◽  
Daniel V. Rocha
Keyword(s):  
Elastic System ◽  
Fractional Power ◽  
Global Attractors ◽  
Memory Term

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).

Global Attractors for Parabolic Problems in Fractional Power Spaces

1995 ◽  
Vol 26 (2) ◽  
pp. 415-427 ◽  
Author(s):  
Alexandre Nolasco De Carvalho ◽  
José Gaspar Ruas-Filho
Keyword(s):  
Fractional Power ◽  
Global Attractors ◽  
Parabolic Problems

Contracting sets and dissipation

1995 ◽  
Vol 125 (6) ◽  
pp. 1305-1329 ◽  
Author(s):  
Alexandre N. Carvalho
Keyword(s):  
Partial Differential Equations ◽  
Fractional Power ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Parabolic Partial Differential Equations ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Invariant Regions

In this work we study reaction–diffusion systems in fractional power spaces Xα which are embedded in L∞. We prove that the solution operators T(t) to these problems are globally defined, point dissipative, locally bounded and compact. That ensures the existence of global attractors. We also find a set containing the range of every function in the attractor, providing good estimates on asymptotic concentrations. This is done under very few hypotheses on the reaction term. These hypotheses are natural and easy to verify in many applications. The tools employed are the theory of invariant regions for systems of parabolic partial differential equations, the notion of contracting sets and the variation of constants formula. Several examples are considered to emphasise the applicability of these techniques.

scholarly journals Theoretical and numerical stability results for a viscoelastic swelling porous-elastic system with past history

2021 ◽  
Vol 6 (11) ◽  
pp. 11921-11949
Author(s):  
Adel M. Al-Mahdi ◽  
◽  
Mohammad M. Al-Gharabli ◽  
Mohamed Alahyane ◽  
◽  
...  
Keyword(s):  
Elastic System ◽  
Past History ◽  
Stability Result ◽  
Kernel Functions ◽  
Memory Term ◽  
Relaxation Kernel ◽  
Wave Speeds ◽  
Swelling Porous Media ◽  
Stability Results ◽  
Theoretical Results

<abstract><p>The purpose of this paper is to establish a general stability result for a one-dimensional linear swelling porous-elastic system with past history, irrespective of the wave speeds of the system. First, we establish an explicit and general decay result under a wider class of the relaxation (kernel) functions. The kernel in our memory term is more general and of a broader class. Further, we get a better decay rate without imposing some assumptions on the boundedness of the history data considered in many earlier results in the literature. We also perform several numerical tests to illustrate our theoretical results. Our output extends and improves some of the available results on swelling porous media in the literature.</p></abstract>

1448: Elastic System Fibers in the Corpora Cavernosa of Potent and Patients with Erectile Dysfunction

2004 ◽  
Vol 171 (4S) ◽  
pp. 381-381
Author(s):  
Waldemar S. Costa ◽  
Fabrício B. Carrerete ◽  
Ronaldo Damião ◽  
Marcia A. Babinski ◽  
Francisco J.B. Sampaio ◽  
...  
Keyword(s):  
Erectile Dysfunction ◽  
Elastic System ◽  
Corpora Cavernosa

Driven elastic system in a random environment

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-69-Pr10-71 ◽  
Author(s):  
P. Chauve ◽  
T. Giamarchi ◽  
P. Le Doussal
Keyword(s):  
Random Environment ◽  
Elastic System

CALCULATION OSCILLATIONS OF VARIOUS ELEMENTS OF THE ELASTIC SYSTEM OF THE CENTER-FREE GRINDING MACHINE SASL 5AD

2020 ◽  
pp. 160-165
Author(s):  
Джугурян Т.Г. ◽  
Марчук В.І. ◽  
Марчук І. В.
Keyword(s):  
Horizontal Plane ◽  
Natural Frequencies ◽  
Elastic System ◽  
Experimental Studies ◽  
Piezoelectric Sensors ◽  
Forced Oscillations ◽  
Method Of Calculation ◽  
Vibration Resistance ◽  
Grinding Machine ◽  
Experimental Researches

During the design of operations of centerless intermittent grinding of surfaces there is a need to identify the natural frequencies of oscillations of the elements of the technological system of grinding. The method of calculation of rigidity, vibration resistance and forced oscillations of the elements of the circular grinding machine is offered in the article. Carrying out of experimental researches of rigidity of elastic system of the SASL 5AD grinding machine. We conducted preliminary experimental studies to measure the oscillations of various elements of the elastic system of the SASL 5AD grinding machine in the horizontal plane by piezoelectric sensors during grinding with continuous and discontinuous circles with different geometric parameters.

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

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