Higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation in non-cylindrical domains

Yan-ping, Xiao; Sun, Chunyou

doi:10.1016/j.na.2014.10.012

Cited by 10 publications

(3 citation statements)

References 13 publications

(38 reference statements)

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“…Since then, there are many researches on the existence criteria of the pullback D-attractor or time-dependent global attractor, as well as their applications in different mathematical physical models (cf. [30,35,36,39,41,43,45] and references therein).…”

Section: Define the Universementioning

confidence: 99%

Continuity of the attractors in time-dependent spaces and applications

Li¹,

Yang²

2022

Preprint

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In this paper, we investigate the continuity of the attractors in time-dependent phase spaces. (i) We establish two abstract criteria on the upper semicontinuity and the residual continuity of the pullback D-attractor with respect to the perturbations, and an equivalence criterion between their continuity and the pullback equi-attraction, which generalize the continuity theory of attractors developed recently in [27,28] to that in time-dependent spaces. (ii) We propose the notion of pullback D-exponential attractor, which includes the notion of time-dependent exponential attractor [33] as its spacial case, and establish its existence and Hölder continuity criterion via quasi-stability method introduced originally by Chueshov and Lasiecka [12,13]. (iii) We apply above-mentioned criteria to the semilinear damped wave equations with perturbed time-dependent speed of propagation: ǫρ(t)u tt + αu t − ∆u + f (u) = g, with perturbation parameter ǫ ∈ (0, 1], to realize above mentioned continuity of pullback D and Dexponential attractors in time-dependent phase spaces, and the method developed here allows to overcome the difficulty of the hyperbolicity of the model. These results deepen and extend recent theory of attractors in time-dependent spaces in literatures [15,20,29].

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Section: Define the Universementioning

confidence: 99%

Continuity of the attractors in time-dependent spaces and applications

Li¹,

Yang²

2022

Preprint

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“…In [15], the existence of pullback D λ 1 attractor defined in time varying domains has been considered. Then we can establish the regularity attraction of (L 2 , L 2 ) pullback D λ 1 attractor.…”

Section: Lemma 31 ([11])mentioning

confidence: 99%

Pullback attraction in $H_{0}^{1}$ for semilinear heat equation in expanding domains

2020

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“…The reaction-diffusion equations and systems are of rigorous significance due to its widespread applications and model formations in various fields [1][2][3][4][5]. In this attempt, we examine a reversible chemical reaction between two species P and Q in a bounded region Ω ⊂ R, the system of PDE forms the reaction-diffusion system [6].…”

Section: Introductionmentioning

confidence: 99%

The reaction dimerization: A resourceful slant applied on the fractional partial differential equation

et al. 2019

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The paper presents an analysis to investigate the time-fractional coupled diffusion equation with non-linear reaction subject to piecewise initial conditions. The governance system is determined analytically, and numerically adopting an artificial neural network taking the Caputo fractional derivative. In this scheme, the differential equations are transformed into an optimization problem, and minimize the problem by using sophisticated computer simulation Nelder-Mead algorithm. Finally, an experiment has been executed in the application of o-phenylenedioxy-dimethylsilane reaction dimerization which is a trial solution of resources as coefficients. The obtained solution is analyzed by tabulation of numerical values and plotting time based graphs. The novelty of the solution will be provided by comparison with the previous work in the literature as a special case. The numerical outcomes demonstrate the momentous features, efficiency and reliability of the approach.

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Higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation in non-cylindrical domains

Cited by 10 publications

References 13 publications

Continuity of the attractors in time-dependent spaces and applications

Continuity of the attractors in time-dependent spaces and applications

Pullback attraction in $H_{0}^{1}$ for semilinear heat equation in expanding domains

The reaction dimerization: A resourceful slant applied on the fractional partial differential equation

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