Asymptotic Dynamical Difference between the Nonlocal and Local Swift-Hohenberg Models

In this paper the difference in the asymptotic dynamics between the nonlocal and local two-dimensional Swift-Hohenberg models is investigated. It is shown that the bounds for the dimensions of the global attractors for the nonlocal and local Swift-Hohenberg models differ by an absolute constant, which depends only on the Rayleigh number, and upper and lower bounds of the kernel of the nonlocal nonlinearity. Even when this kernel of the nonlocal operator is a constant function, the dimension bounds of the global attractors still differ by an absolute constant depending on the Rayleigh number.Comment: 13 pages, LaTex fil

The pullback attractors for the Higher-order Kirchhoff-type equation with strong linear damping

The paper investigates pullback the attractors for the Higher-order Kirchhoff-type equation with strong linear damping:.Firstly, we do priori estimation for the equations to obtain the existence and uniqueness of the solution inby some assumptions the Galerkin method. Then, we prove existence of the pullback attractorsin

The global attractors and their Hausdorff and fractal dimensions estimation for the higher-order nonlinear Kirchhoff-type equation*

We investigate the global well-posedness and the longtime dynamics of solutions for the higher-order Kirchhoff-typeequation with nonlinear strongly dissipation:2( ) ( )m mt t tu   ï„ u  ï¦ ï D u ï ( ) ( ) ( )m ï„ u  g u  f x . Under of the properassume, the main results are that existence and uniqueness of the solution is proved by using priori estimate and Galerkinmethod, the existence of the global attractor with finite-dimension, and estimation Hausdorff and fractal dimensions of theglobal attractor

The Global Attractors For The Higher-order Kirchhoff-type Equation With Nonlinear Strongly Damped Term

The paper studies the longtime behavior of solutions to the initial boundary value problem for a class of Higher-order Kirchhoff models: For strong nonlinear damping and , we make assumptions (H1)-(H3). are nonlinear function specified later , we make assumptions (G1)-(G3). Under of the proper assume, the main results are existence and uniqueness of the solution are proved , and deal with the global attractors in natural energy space

The global attractors and dimensions estimation for the Kirchho type wave equations with nonlinear strongly damped terms

This paper studies the long time behavior of the solution to the initial boundaryvalue problems for a class of strongly damped Kirchho type wave equations:utt "1ut + j ut jp1 ut + j u jq1 u (kruk2)u = f(x):Firstly, we prove the existence and uniqueness of the solution by priori estimate and the Galerkin method. Then we obtain to the existence of the global attractor. Finally, we consider that the estimation of the upper bounds of Hausdor and fractal dimensionsfor the global attractor is obtained

Apolipoprotein E ε4 accelerates the longitudinal cerebral atrophy in open access series of imaging studies-3 elders without dementia at enrollment

IntroductionEarly studies have reported that APOE is strongly associated with brain atrophy and cognitive decline among healthy elders and Alzheimer’s disease (AD). However, previous research has not directly outlined the modulation of APOE on the trajectory of cerebral atrophy with aging during the conversion from cognitive normal (CN) to dementia (CN2D).MethodsThis study tried to elucidate this issue from a voxel-wise whole-brain perspective based on 416 qualified participants from a longitudinal OASIS-3 neuroimaging cohort. A voxel-wise linear mixed-effects model was applied for detecting cerebrum regions whose nonlinear atrophic trajectories were driven by AD conversion and to elucidate the effect of APOE variants on the cerebral atrophic trajectories during the process.ResultsWe found that CN2D participants had faster quadratically accelerated atrophy in bilateral hippocampi than persistent CN. Moreover, APOE ε4 carriers had faster-accelerated atrophy in the left hippocampus than ε4 noncarriers in both CN2D and persistent CN, and CN2D ε4 carriers an noncarriers presented a faster atrophic speed than CN ε4 carriers. These findings could be replicated in a sub-sample with a tough match in demographic information.DiscussionOur findings filled the gap that APOE ε4 accelerates hippocampal atrophy and the conversion from normal cognition to dementia