Results 301 to 310 of about 1,344,372 (340)

Exponential Attractors in Contact Problems

2016
In this chapter we consider two examples of contact problems. First, we study the problem of time asymptotics for a class of two-dimensional turbulent boundary driven flows subject to the Tresca friction law which naturally appears in lubrication theory.
Grzegorz Łukaszewicz, Piotr Kalita
openaire   +2 more sources

Finite‐dimensional attractors and exponential attractors for degenerate doubly nonlinear equations

Mathematical Methods in the Applied Sciences, 2009
AbstractWe consider the following doubly nonlinear parabolic equation in a bounded domain Ω⊂ℝ3:where the nonlinearityfis allowed to have a degeneracy with respect to ∂tuof the form ∂tu|∂tu|pat some pointsx∈Ω.Under some natural assumptions on the nonlinearitiesfandg, we prove the existence and uniqueness of a solution of that problem and establish the ...
Efendiev, M, Zelik, S
openaire   +3 more sources

Exponential Attractors for the Generalized Ginzburg-Landau Equation

Acta Mathematica Sinica, 2000
In this paper, we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial dimensions. We show the squeezing property and the existence of finite dimensional exponential attractors for this ...
Bixiang Wang, Boling Guo
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A uniformly exponential random forward attractor which is not a pullback attractor

Archiv der Mathematik, 2002
A compact random set is constructed which is invariant with respect to a random dynamical system, and which is an exponential forward attractor, but fails to be a pullback attractor.
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Random Exponential Attractor for the 3D Non-autonomous Stochastic Damped Navier–Stokes Equation

Journal of Dynamics and Differential Equations, 2021
Zongfei Han, Shengfan Zhou
semanticscholar   +1 more source

Exponential attractors for the strongly damped wave equations

Nonlinear Analysis: Real World Applications, 2010
Abstract For the strongly damped wave equation with critical nonlinearity, we first show the existence of a ( H 0 1 ( Ω ) × L 2 ( Ω ) , H 0 1 ( Ω ) × H 0 1 ( Ω ) ) -global attractor when the external forcing g ∈ H − 1 ; then we prove that for each T > 0 ...
Meihua Yang, Chunyou Sun
openaire   +2 more sources

Approximation of exponential order of the attractor of a turbulent flow

Physica D: Nonlinear Phenomena, 1994
Abstract In this work, we consider the two-dimensional Navier-Stokes equations with periodic boundary conditions, describing the evolution of homogeneous turbulent flows. We use the method of Debussche and Temam [A. Debussche and R. Temam, convergent families of approximate inertial manifolds, J. Math. Pures Appl., to appear] to construct approximate
T. Dubois, Arnaud Debussche
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Exponential attractors and their relevance to fluid dynamics systems

Physica D: Nonlinear Phenomena, 1993
Abstract In this note we expose some of the recent results in the mathematical theory of infinite dimensional dynamical systems as they pertain to some of the equations of fluid mechanics. Our main objective is to highlight the theory of exponential attractors and discuss its possible significance in the study of 2D incompressible NS equations.
Ciprian Foias, Ciprian Foias, Zhen-Su She, Zhen-Su She, Alp Eden, Basil Nicolaenko, Basil Nicolaenko   +6 more
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Exponential attractor for the delayed logistic equation with a nonlinear diffusion

, 2003
We study the generalized logistic equation where the feedback is captured by the time convolution with a nonnegative measure and the diffusion is the laplacian plus the p-laplacian with $p >= 2$. We prove that the equation has an exponential attractor
D. Pražák
semanticscholar   +1 more source

Exponential attractors for the strongly damped wave equation

Applied Mathematics and Computation, 2013
In this paper, we study the longtime dynamics to a strongly damped wave equation. First, in the critical case, we prove by the l-trajectories method that the related solution semigroup has the exponential attractor. Second, in the subcritical case, we give an explicit upper bound of the fractal dimension of the exponential attractor in terms of the ...
Zhijian Yang, Ke Li
openaire   +2 more sources