Results 231 to 240 of about 2,999 (259)

Exponential attractors for semiconductor equations

2006
This paper studies the asymptotic behaviour of solutions to the classical semiconductor equations due to Shockley. We will construct not only global solutions but also exponential attractors for the dynamical system determined from the Cauchy problem.
FAVINI, ANGELO, A. . LORENZI, A. YAGI
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Exponential attractors for a partially dissipative reaction system

Asymptotic Analysis, 1996
After having established the existence of smooth absorbing sets, thanks to suitable a priori estimates, we obtain for a class of partially dissipative reaction systems a property known as squeezing property. This last leads to the existence of exponential attractors for which the fractal dimension is finite.
Fabrie, P., Galusinski, C.
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Exponential Attractor for a Class of Nonclassical Diusion Equation

Journal of Partial Differential Equations, 2003
In this paper, the following initial boundary value problem of the nonclassical diffusion equation \[ u_t-\nu\Delta u_t- \lambda\Delta u+ g(u)= f(x),\quad (x,t)\in \Omega\times \mathbb{R}^+,\tag{1} \] \[ u(x,0)= u_0(x),\quad x\in\Omega, \] \[ u(x,t)= 0,\quad (x,t)\in \partial\Omega\times \mathbb{R}^+ \] is considered, where \(\lambda\) is a positive ...
Shang, Yadong, Guo, Boling
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Finite-Dimensional Attractors and Exponential Attractors for the Navier--Stokes Equations of Compressible Flow

SIAM Journal on Mathematical Analysis, 2003
Summary: We prove that the uniform attractor for the Navier-Stokes equations of compressible flow with quasi-periodic external forces has finite fractal dimension. As a byproduct of our analysis, we also obtain the existence of finite-dimensional exponential attractors for the Navier-Stokes system.
David Hoff, Mohammed B. Ziane
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Pullback exponential attractors with admissible exponential growth in the past

Nonlinear Analysis: Theory, Methods & Applications, 2014
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Pullback Exponential Attractors for Nonautonomous Reaction–Diffusion Equations

International Journal of Bifurcation and Chaos, 2015
This paper presents a necessary and sufficient condition to prove the existence of the pullback exponential attractor. The asymptotic a priori estimate method is used to produce an abstract result on the existence of the pullback exponential attractor in a strong space without regularity. The established results are illustrated by applying them to the
Xingjie Yan, Wei Qi
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Exponential attractor for a planar shear‐thinning flow

Mathematical Methods in the Applied Sciences, 2007
AbstractWe study the dynamics of an incompressible, homogeneous fluid of a power‐law type, with the stress tensor T = ν(1 + µ|Dv|)p−2Dv, where Dv is a symmetric velocity gradient. We consider the two‐dimensional problem with periodic boundary conditions and p ∈ (1, 2).
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Exponential attractors for extensible beam equations

Nonlinearity, 1993
The authors transfer ideas and results of the classical theory of dynamical systems for ODE to a class of nonlinear dynamical boundary value problems for PDE which includes equations looking like beam and plate equations. They establish the existence of a compact attractor and some of its properties for this class of systems using energy methods and ...
Eden, A., Milani, A. J.
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A global attractor consisting of exponentially unstable equilibria

2013 American Control Conference, 2013
There exist examples in the literature of attractors consisting solely of unstable equilibria, but in these examples, the unstable equilibria are not exponentially unstable (the differentials of the vector fields at the unstable equilibria have no eigenvalues in the open right-half complex plane).
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Exponential attractors for semigroups in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 2012
The authors discussed the existence of exponential attractors for abstract semigroups in Banach spaces. Let \(X\) be a Banach space, \(\{S(t)\;|\;t\geq 0\}\) be a semigroup on \(X\), \(\mathcal{A}\) be the global attractor of \(\{S(t)\;|\;t\geq 0\}\), and \(B_{\varepsilon_0}(\mathcal{A})\) denote the \(\varepsilon_0\)-neighborhood of \(\mathcal{A}\) in
Zhong, Yansheng, Zhong, Chengkui
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