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Accurate Computations On Inertial Manifolds
 Phys. Lett. A
"... . An algorithm for the computation of inertial manifolds is implemented. The effects of certain algorithm parameters are illustrated on an ordinary differential equation where an exact manifold is known. The algorithm is then applied to the KuramotoSivashinsky equation to recover the high wave numb ..."
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Cited by 42 (8 self)
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. An algorithm for the computation of inertial manifolds is implemented. The effects of certain algorithm parameters are illustrated on an ordinary differential equation where an exact manifold is known. The algorithm is then applied to the KuramotoSivashinsky equation to recover the high wave
On the Negative Invariance of Inertial Manifolds
, 1998
"... The present paper is concerned with sufficient conditions for the negative invariance of inertial manifolds. The solution operators of the underlying nonlinear dissipative partial differential equation are assumed to be injective. We give an equivalent condition for a positive invariant manifold to ..."
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The present paper is concerned with sufficient conditions for the negative invariance of inertial manifolds. The solution operators of the underlying nonlinear dissipative partial differential equation are assumed to be injective. We give an equivalent condition for a positive invariant manifold
Inertial manifolds and the cone condition
 Dynam. Systems Appl
, 1993
"... ABSTRACT: The “cone condition”, used in passing in many proofs of the existence of inertial manifolds, is examined in more detail. Invariant manifolds for dissipative flows can be obtained directly using no other dynamical information. After finding a condition for the exponential attraction of traj ..."
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Cited by 2 (0 self)
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ABSTRACT: The “cone condition”, used in passing in many proofs of the existence of inertial manifolds, is examined in more detail. Invariant manifolds for dissipative flows can be obtained directly using no other dynamical information. After finding a condition for the exponential attraction
Computing inertial manifolds
 Discrete and Continuous Dynamical Systems
, 1995
"... Abstract. This paper discusses two numerical schemes that can be used to approximate inertial manifolds whose existence is given by one of the standard methods of proof. The methods considered are fully numerical, in that they take into account the need to interpolate the approximations of the manif ..."
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Cited by 3 (1 self)
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Abstract. This paper discusses two numerical schemes that can be used to approximate inertial manifolds whose existence is given by one of the standard methods of proof. The methods considered are fully numerical, in that they take into account the need to interpolate the approximations
Inertial Manifolds With And Without Delay
, 1999
"... This article discusses the relationship between the inertial manifolds "with delay" introduced by Debussche & Temam, and the standard definition. In particular, the "multivalued" manifold of the same paper is shown to arise naturally from the manifolds "with delay" ..."
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Cited by 2 (0 self)
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This article discusses the relationship between the inertial manifolds "with delay" introduced by Debussche & Temam, and the standard definition. In particular, the "multivalued" manifold of the same paper is shown to arise naturally from the manifolds "with delay
Inertial Manifolds Under Multistep Discretization
, 1998
"... . Finitedimensional inertial manifolds attract solutions to a nonlinear parabolic differential equation at an exponential rate. In this paper inertial manifolds for multistep discretizations of such equations are studied. We provide an existence result for inertial manifolds under multistep discret ..."
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. Finitedimensional inertial manifolds attract solutions to a nonlinear parabolic differential equation at an exponential rate. In this paper inertial manifolds for multistep discretizations of such equations are studied. We provide an existence result for inertial manifolds under multistep
Approximate inertial manifolds of exponential order
 Discrete and Continuous Dynamical Systems
, 1995
"... Abstract. A fairly general class of nonlinear evolution equations with a selfadjoint or non selfadjoint linear operator is considered, and a family of approximate inertial manifolds (AIMs) is constructed. Two cases are considered: when the spectral gap condition (SGC) is not satisfied and an exact ..."
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Cited by 11 (6 self)
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Abstract. A fairly general class of nonlinear evolution equations with a selfadjoint or non selfadjoint linear operator is considered, and a family of approximate inertial manifolds (AIMs) is constructed. Two cases are considered: when the spectral gap condition (SGC) is not satisfied
CHAPTER 3 INERTIAL MANIFOLDS AND
"... The understanding of the long term behavior of solutions of nonlinear evolutionary systems is of great importance in the study of the natural sciences. The dynamics of such nonlinear systems is expected to be complicated and is often associated to chaos and turbulence. In the Dynamical Systems appr ..."
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The understanding of the long term behavior of solutions of nonlinear evolutionary systems is of great importance in the study of the natural sciences. The dynamics of such nonlinear systems is expected to be complicated and is often associated to chaos and turbulence. In the Dynamical Systems approach to tur
CHAPTER 3 INERTIAL MANIFOLDS AND
"... Introduction The understanding of the long term behavior of solutions of nonlinear evolutionary systems is of great importance in the study of the natural sciences. The dynamics of such nonlinear systems is expected to be complicated and is often associated to chaos and turbulence. In the Dynamical ..."
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Introduction The understanding of the long term behavior of solutions of nonlinear evolutionary systems is of great importance in the study of the natural sciences. The dynamics of such nonlinear systems is expected to be complicated and is often associated to chaos and turbulence. In the Dynamical Systems approach to turbulence, the chaotic behavior is explained by the wandering of the orbits around a complicated attractor. In other words, in the simplest regimes, the orbits converge either to a xed point or to a periodic motion, while in the chaotic regimes, the orbits converge to a more complicated attractor, possibly with a fractal structure. Such chaotic behaviors lead to an extreme sensitivity to perturbations of the initial data, which in turn aects considerably the predictability of the long term behavior of the system. This sensitivity is already present in some lowdimensional systems such as the threedimensional Lorenz system, and is expected to increase dramatically whe
Results 1  10
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154