Global attractor for some partial functional differential equations with finite delay

You, Honglian; Yuan, Rong

doi:10.1016/j.na.2009.12.027

Cited by 9 publications

(7 citation statements)

References 17 publications

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“…The existence of attractor for semilinear or nonlinear partial functional differential equations including (3.34) as special case have been reported in much literature. See, for instance, [13] tackle the autonomous case with a nondensely defined linear part. Apparently, (3.34) satisfies other assumptions in [13] and hence it follows from Proposition 3.1 and Theorem 3.1 in [13] that (3.34) admits a global attractor, implying the existence of positive invariant absorbing set which is stated in the following.…”

Section: Retarded Reaction-diffusion Equationmentioning

confidence: 99%

“…See, for instance, [13] tackle the autonomous case with a nondensely defined linear part. Apparently, (3.34) satisfies other assumptions in [13] and hence it follows from Proposition 3.1 and Theorem 3.1 in [13] that (3.34) admits a global attractor, implying the existence of positive invariant absorbing set which is stated in the following. We now construct exponential attractor based on the global attractor B obtained in Lemma 3.2.…”

Section: Retarded Reaction-diffusion Equationmentioning

confidence: 99%

See 1 more Smart Citation

Exponential pullback attractors with explicit fractal dimensions for functional differential equations in Banach spaces

Hu¹,

Caraballo²

2023

Preprint

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The aim of this paper is to propose a new method to construct exponential attractors for infinite dimensional dynamical systems in Banach spaces with explicit fractal dimension.The approach is established by combing the squeezing properties and the covering of finite subspace of Banach spaces, which generalize the method established in Hilbert spaces. The constructed exponential attractors possess explicit fractal dimensions which do not depend on the entropy number but only depend on the spectrum of the linear part and Lipschitz constant of the nonlinear part. The method is especially effective for functional differential equations in Banach spaces for which sate decomposition of the linear part can be adopted to prove squeezing property. The theoretical results are applied to the retarded functional differential equation and retarded reaction-diffusion equations.

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Section: Retarded Reaction-diffusion Equationmentioning

confidence: 99%

Section: Retarded Reaction-diffusion Equationmentioning

confidence: 99%

Exponential pullback attractors with explicit fractal dimensions for functional differential equations in Banach spaces

Hu¹,

Caraballo²

2023

Preprint

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“…The following dynamical notions are from [6]. You and Yuan [11] proved the existence of a global attractor of (2.1) by using the following.…”

Section: Lemma 27 Under the Conditions (H1) And (H2) (21) Has A Umentioning

confidence: 99%

“…Also, Bouzahir et al studied the existence of a global attractor for (1.2) under the initial condition x 0 = ϕ ∈ C γ in [2]. You and Yuan [11] investigated the existence of a global attractor for (1.2) under the initial condition…”

Section: Introductionmentioning

confidence: 99%

Existence of Global Attractor for Cauchy Problems

Choi¹,

Jang²,

Koo³

et al. 2013

Journal of the Chungcheong Mathematical Society

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“…On the other hand, it is known that attractors are a very useful tool (valid in more general situations than for stability) in investigating the asymptotical be-havior of solutions. However, as far as we know, most of existing results deal with the existence of attractors in the case of finite delay (see, for example, [4,13,14,15,17,22]); only very few papers [6,7] deal with the case of infinite delay in some concrete phase spaces.…”

mentioning

confidence: 99%