scholarly journals PULLBACK ATTRACTORS FOR A NONAUTONOMOUS INTEGRO-DIFFERENTIAL EQUATION WITH MEMORY IN SOME UNBOUNDED DOMAINS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350042
Author(s):  
MARÍA ANGUIANO ◽  
TOMÁS CARABALLO ◽  
JOSÉ REAL ◽  
JOSÉ VALERO
Keyword(s):  
Unbounded Domains ◽  
Memory Term ◽  
Pullback Attractors ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Diffusion Type ◽  
Nonautonomous Dynamical Systems ◽  
Infinite Delays ◽  
Convolution Integrals ◽  
With Memory

The main aim of this paper is to analyze the asymptotic behavior of a nonautonomous integro-differential parabolic equation of diffusion type with a memory term, expressed by convolution integrals involving infinite delays, in an unbounded domain. The assumptions imposed do not ensure uniqueness of solutions of the corresponding initial value problems. The theory of set-valued nonautonomous dynamical systems is applied to prove the existence of pullback attractors for our model. To do this, we first analyze an abstract version of the equation.

DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION

2012 ◽  
Vol 22 (02) ◽  
pp. 1150012 ◽  
Author(s):  
YONGQIN LIU ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Decay Estimate ◽  
Pointwise Estimate ◽  
Decay Property ◽  
Memory Term ◽  
Fourier Space ◽  
Initial Value ◽  
Timoshenko System ◽  
Frictional Dissipation ◽  
Memory Type ◽  
With Memory

In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier–Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

scholarly journals Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

2020 ◽  
Vol 66 (4) ◽  
pp. 773-793 ◽  
Author(s):  
Arman Shojaei ◽  
Alexander Hermann ◽  
Pablo Seleson ◽  
Christian J. Cyron
Keyword(s):  
Boundary Conditions ◽  
Materials Science ◽  
Unbounded Domains ◽  
Diffusion Models ◽  
Absorbing Boundary Conditions ◽  
The Finite Element Method ◽  
Absorbing Boundary ◽  
Diffusion Type ◽  
2D And 3D ◽  
Accuracy And Stability

Abstract Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

scholarly journals Exponential Attractors for the 3D Fractional-order Bardina Turbulence Model With Memory and Horizontal Filtering

2021 ◽  
Author(s):  
Michele Annese ◽  
Luca Bisconti ◽  
Davide Catania
Keyword(s):  
Phase Space ◽  
Fractional Order ◽  
Turbulence Model ◽  
Memory Term ◽  
Exponential Attractor ◽  
Exponential Attractors ◽  
Regularity Properties ◽  
Hereditary Effects ◽  
With Memory ◽  
Simplified Bardina

AbstractWe consider the 3D simplified Bardina turbulence model with horizontal filtering, fractional dissipation, and the presence of a memory term incorporating hereditary effects. We analyze the regularity properties and the dissipative nature of the considered system and, in our main result, we show the existence of a global exponential attractor in a suitable phase space.

Walrasian Equilibrium Problem with Memory Term

2011 ◽  
Vol 151 (1) ◽  
pp. 64-80 ◽  
Author(s):  
Maria Bernadette Donato ◽  
Monica Milasi ◽  
Laura Scrimali
Keyword(s):  
Equilibrium Problem ◽  
Walrasian Equilibrium ◽  
Memory Term ◽  
With Memory
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