Your search for: 'author:("Yang, Xin-Guang")' has returned 4 results. (0.046s) Save search

Authors: Yan, Xingjie | Wang, Shubin | Yang, Xin-Guang | Zhang, Junzhao

Article Type: Research Article

Abstract: This paper is concerned with the long time behavior of solutions for a non-autonomous reaction-diffusion equations with anomalous diffusion. Under suitable assumptions on nonlinearity and external force, the global well-posedness has been studied. Then the pullback attractors in L 2 ( Ω ) and H 0 α ( Ω ) (0 < α < 1 ) have been achieved with a restriction on the growth order of nonlinearity as 2 ⩽ p ⩽ 2 ( n − α ) n − 2 α . The results presented can be seen as the extension for classical theory of infinite dimensional dynamical …system to the fractional diffusion equations. Show more

Keywords: Fractional Laplacian, pullback attractor, non-compactness measure

DOI: 10.3233/ASY-221800

Citation: Asymptotic Analysis, vol. 132, no. 3-4, pp. 495-517, 2023

Authors: Su, Keqin | Yang, Xin-Guang | Miranville, Alain | Yang, He

Article Type: Research Article

Abstract: This paper is concerned with the dynamics of the two-dimensional Navier–Stokes equations with multi-delays in a Lipschitz-like domain, subject to inhomogeneous Dirichlet boundary conditions. The regularity of global solutions and of pullback attractors, based on tempered universes, is established, extending the results of Yang, Wang, Yan and Miranville (Discrete Contin. Dyn. Syst. 41 (2021 ) 3343–3366). Furthermore, the robustness of pullback attractors when the delays, considered as small perturbations, disappear is also derived. The key technique in the proofs is the application of a retarded Gronwall inequality and a variable index for the tempered pullback dynamics, allowing to obtain uniform …estimates and the compactness of the process. Show more

Keywords: Navier–Stokes equations, multi-delays, Lipschitz-like domain, robustness

DOI: 10.3233/ASY-231845

Citation: Asymptotic Analysis, vol. 134, no. 3-4, pp. 513-552, 2023

Authors: Zhao, Mingxia | Yang, Xin-Guang | Yan, Xingjie | Cui, Xiaona

Article Type: Research Article

Abstract: This paper is concerned with the tempered pullback dynamics for a three dimensional Benjamin–Bona–Mahony equations with sublinear operator on bounded domain, which describes the long time behavior for long waves model in shallow water with friction. By virtue of a new retarded Gronwall inequality, and using the energy equation method from J.M. Ball (Disc. Cont. Dyn. Syst. 10 (2004 ) 31–52) to achieve asymptotic compactness for solution process, the minimal family of pullback attractors has been obtained, which reduces a single trajectory under a sufficient condition.

Keywords: Benjamin–Bona–Mahony equation, uniformly asymptotic stable, pullback attractors

DOI: 10.3233/ASY-201601

Citation: Asymptotic Analysis, vol. 121, no. 1, pp. 75-100, 2021

Authors: Li, Lu | Yang, Xin-Guang | Li, Xuezhi | Yan, Xingjie | Lu, Yongjin

Article Type: Research Article

Abstract: The tempered pullback dynamics of the 3D Brinkman–Forchheimer equation with variable delay has been studied in this paper. With the different universes which has some topology property, the existence of minimal and unique family of pullback attractors were obtained. Moreover, the convergence of pullback attractors for the 3D Brinkman–Forchheimer equation as delay term vanishes is also been proved, i.e., the upper semi-continuity of attractors.

Keywords: Brinkman–Forchheimer equation, delay, upper semi-continuity, universe, tempered pullback attractors

DOI: 10.3233/ASY-181512

Citation: Asymptotic Analysis, vol. 113, no. 3, pp. 167-194, 2019