Robust exponential attractors for the non-autonomous nonclassical diffusion equation with memory

2013 ◽  
Vol 28 (4) ◽  
pp. 501-517 ◽  
Author(s):  
Li-xia Pan ◽  
Yong-feng Liu
Keyword(s):  
Diffusion Equation ◽  
Exponential Attractors ◽  
Nonclassical Diffusion Equation ◽  
With Memory

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.

On a stochastic nonclassical diffusion equation with standard and fractional Brownian motion

2021 ◽  
pp. 2140011
Author(s):  
Tomás Caraballo ◽  
Tran Bao Ngoc ◽  
Tran Ngoc Thach ◽  
Nguyen Huy Tuan
Keyword(s):  
Brownian Motion ◽  
Diffusion Equation ◽  
Stochastic Integrals ◽  
Well Posedness ◽  
Time Data ◽  
Final Time ◽  
Fractional Brownian Motions ◽  
Nonclassical Diffusion Equation ◽  
Definition Of ◽  
Well Posed

This paper is concerned with the mathematical analysis of terminal value problems (TVP) for a stochastic nonclassical diffusion equation, where the source is assumed to be driven by classical and fractional Brownian motions (fBms). Our two problems are to study in the sense of well-posedness and ill-posedness meanings. Here, a TVP is a problem of determining the statistical properties of the initial data from the final time data. In the case [Formula: see text], where [Formula: see text] is the fractional order of a Laplace operator, we show that these are well-posed under certain assumptions. We state a definition of ill-posedness and obtain the ill-posedness results for the problems when [Formula: see text]. The major analysis tools in this paper are based on properties of stochastic integrals with respect to the fBm.

scholarly journals Homogenization limit for the Diffusion Equation in a domain Perforated along (n - 1)-Dimensional Manifold with Dynamic Conditions on the Boundary of the Perforations: Critical Case

2019 ◽  
Vol 486 (1) ◽  
pp. 12-19
Author(s):  
M. N. Zubova ◽  
T. A. Shaposhnikova
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Critical Case ◽  
Original Problem ◽  
Dimensional Manifold ◽  
Dynamic Boundary Conditions ◽  
Dynamic Conditions ◽  
Convergence Of Solutions ◽  
Homogenization Model ◽  
With Memory

The problem of homogenization the diffusion equation in a domain perforated along an (n - 1)-dimensional manifold with dynamic boundary conditions on the boundary of the perforations is studied. A homogenization model is constructed that is a transmission problem for the diffusion equation with the transmission conditions containing a term with memory. A theorem on the convergence of solutions of the original problem to the solution of the homogenized one is proved.

On Time Fractional Diffusion Equation with Memory Term

2021 ◽  
Vol 30 (1) ◽  
Author(s):  
Nguyen Duc Phuong ◽  
Nguyen Anh Tuan ◽  
Tran Thanh Binh ◽  
Tran Ngoc Thach
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Memory Term ◽  
Time Fractional Diffusion Equation ◽  
With Memory

Global Attractors for a Nonclassical Diffusion Equation

2007 ◽  
Vol 23 (7) ◽  
pp. 1271-1280 ◽  
Author(s):  
Chun You Sun ◽  
Su Yun Wang ◽  
Cheng Kui Zhong
Keyword(s):  
Diffusion Equation ◽  
Global Attractors ◽  
Nonclassical Diffusion Equation
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