- 作 者: ( "chunyou sun" OR "chun-you sun" )
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Stability for a Class of Extensible Beams with Degenerate Nonlocal DampingThe Journal of Geometric Analysis (IF 1.1) Pub Date : 2023-07-03 , DOI:10.1007/s12220-023-01353-3Cong Zhou, Chunyou SunThis paper investigates the well-posedness and stability of the beam model with degenerate nonlocal damping: \( u_{tt}+\Delta ^2u-M(\Vert \nabla u\Vert ^2)\Delta u+(\Vert \Delta u\Vert ^\theta +q\Vert u_t\Vert ^\rho )(-\Delta )^\delta u_t+f(u)=0\ \ \hbox {in} \ \ \Omega \times {\mathbb {R}}^+,\) where \(\Omega \subset {\mathbb {R}}^n\) is a bounded domain with smooth boundary, \(\theta \ge 1,~q\ge ...
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Stability for a Class of Extensible Beams with Degenerate Nonlocal DampingJournal of Geometric Analysis Pub Date : 2023-07-03 , DOI:10.1007/s12220-023-01353-3Cong Zhou, Chunyou SunThis paper investigates the well-posedness and stability of the beam model with degenerate nonlocal damping: \( u_{tt}+\Delta ^2u-M(\Vert \nabla u\Vert ^2)\Delta u+(\Vert \Delta u\Vert ^\theta +q\Vert u_t\Vert ^\rho )(-\Delta )^\delta u_t+f(u)=0\ \ \hbox {in} \ \ \Omega \times {\mathbb {R}}^+,\) where \(\Omega \subset {\mathbb {R}}^n\) is a bounded domain with smooth boundary, \(\theta \ge 1,~q\ge ...
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Analysis of mass controlled reaction–diffusion systems with nonlinearities having critical growth ratesJournal of Evolution Equations (IF 1.4) Pub Date : 2023-06-06 , DOI:10.1007/s00028-023-00894-yChunyou Sun, Bao Quoc Tang, Juan Yang
We analyze semilinear reaction–diffusion systems that are mass controlled, and have nonlinearities that satisfy critical growth rates. The systems under consideration are only assumed to satisfy natural assumptions, namely the preservation of non-negativity and a control of the total mass. It is proved in dimension one that if nonlinearities have (slightly super-) cubic growth rates then the system
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The slightly compressible Brinkman-Forcheimer equations and its incompressible approximationApplied Mathematics Letters (IF 3.7) Pub Date : 2023-04-06 , DOI:10.1016/j.aml.2023.108669Xinhua Li, Chunyou SunThis paper investigates the slightly compressible Brinkman–Forchheimer equations (BFEs): ∂tu−Δxu+∇xp+f(u)=g with D−1(t)∂tp+divu=0 in a bounded 3D domain with Dirichlet boundary conditions. The features of this problem is that, formally, this system is partially dissipative, and will recover to incompressible BFEs when the time-dependent coefficient D(t) goes to infinity as t→∞. The well-posedness and ...
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Kolmogorov $\varepsilon$-entropy of the uniform attractor for a wave equationarXiv - MATH - Dynamical Systems Pub Date : 2023-03-06 , DOI:arxiv-2303.02991Yangmin Xiong, Chunyou SunThis paper is concerned with a non-autonomous sup-cubic semilinear wave equation in a smooth bounded domain of $\mathbb R^{3}$, using the introduced weak topology entropy, we obtain an upper bound for the $\varepsilon$-entropy of the uniform attractor for the case where the external forces are not translation-compact. ...
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Entropy estimates for uniform attractors of 2D Navier–Stokes equations with weakly normal measuresStochastics and Dynamics (IF 1.1) Pub Date : 2023-02-03 , DOI:10.1142/s0219493722400366Yangmin Xiong, Xiaoya Song, Chunyou SunThis paper aims at the long-time behavior of non-autonomous 2D Navier–Stokes equations with a class of external forces which are H-valued measures in time. We first establish the well-posedness of solutions as well as the existence of a strong uniform attractor, and then pay the main attention on the estimation of 𝜀-entropy for such uniform attractor in the standard energy phase space. ...
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Uniform attractors for nonautonomous 2D MHD equations with partial dissipationJournal of Mathematical Physics (IF 1.3) Pub Date : 2022-10-17 , DOI:10.1063/5.0063223Jinfang He, Shan Ma, Chunyou Sun, Lu Yang
In this article, we study the long-time behavior of solutions of nonautonomous 2D magnetohydrodynamics equations with partial dissipation and time-dependent external forcing, which is weakly normal. We prove that the system possesses strong uniform attractors. Furthermore, the structure of the uniform attractors is obtained, and the fractal dimension is estimated for the kernel sections of the uniform
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Variable Hardy Spaces on Non-tangentially Accessible Domains and Their Applications to Div-Curl LemmaThe Journal of Geometric Analysis (IF 1.1) Pub Date : 2022-09-23 , DOI:10.1007/s12220-022-01025-8Xiong Liu, Chunyou Sun, Sibei YangLet \(n\ge 2\), \(\Omega \subset {\mathbb {R}}^n\) be a bounded non-tangentially accessible domain, and \(p(\cdot ):{\mathbb {R}}^n\rightarrow (0,\infty )\) a variable exponent function satisfying \(00}\) generated by \(L_D\). Thirdly, as applications, the authors prove the boundedness of the Riesz transform \(\nabla L_D^{-1/2}\) on the variable Lebesgue space \(L^{p(\cdot )}(\Omega )\) when \(1 ...
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Variable Hardy Spaces on Non-tangentially Accessible Domains and Their Applications to Div-Curl LemmaJournal of Geometric Analysis Pub Date : 2022-09-23 , DOI:10.1007/s12220-022-01025-8Xiong Liu, Chunyou Sun, Sibei YangLet \(n\ge 2\), \(\Omega \subset {\mathbb {R}}^n\) be a bounded non-tangentially accessible domain, and \(p(\cdot ):{\mathbb {R}}^n\rightarrow (0,\infty )\) a variable exponent function satisfying \(00}\) generated by \(L_D\). Thirdly, as applications, the authors prove the boundedness of the Riesz transform \(\nabla L_D^{-1/2}\) on the variable Lebesgue space \(L^{p(\cdot )}(\Omega )\) when \(1 ...
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Dynamics for 2D incompressible Navier–Stokes flow coupled with time-dependent Darcy flowJournal of Mathematical Physics (IF 1.3) Pub Date : 2022-06-17 , DOI:10.1063/5.0057973Yang Liu, Shan Ma, Chunyou SunIn this paper, we use the method of evolutionary systems introduced by Cheskidov and Foias to describe the existence of global attractor for 2D incompressible Navier–Stokes flow coupled with time-dependent Darcy flow. Furthermore, stationary statistical solutions of this system are constructed from the global attractor. ...
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Non-concentration phenomenon reaction-diffusion systems with mass dissipationarXiv - MATH - Analysis of PDEs Pub Date : 2022-05-05 , DOI:arxiv-2205.02498Anna Kostianko, Chunyou Sun, Bao Quoc Tang, Juan Yang, Sergey ZelikReaction-diffusion systems with mass dissipation are known to possess blow-up solutions in higher dimensions when the nonlinearities have super quadratic growth rates. In dimension one, it has been shown recently that one can have global existence of bounded solutions if nonlinearities are at most cubic. For the cubic intermediate sum condition, i.e. nonlinearities might have arbitrarily high growth ...
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Well-posedness and attractors for a 2D Boussinesq system with partial dissipationJournal of Differential Equations (IF 2.4) Pub Date : 2022-02-28 , DOI:10.1016/j.jde.2022.02.045Jinfang He, Shan Ma, Chunyou SunThis article is devoted to the global well-posedness and the long-time behavior of solutions of a 2D Boussinesq equations with partial dissipation. We prove that this system is global well-posed under some weaker assumptions on the initial data and has a weak sigma-attractor which retains some of the common properties of global attractors for the dissipative dynamical system, moreover, the local attractor ...
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Inertial Manifolds via Spatial Averaging RevisitedSIAM Journal on Mathematical Analysis (IF 2.0) Pub Date : 2022-01-04 , DOI:10.1137/20m1375437Anna Kostianko, Xinhua Li, Chunyou Sun, Sergey Zelik
SIAM Journal on Mathematical Analysis, Volume 54, Issue 1, Page 268-305, January 2022. The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by Sell and Mallet-Paret. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number
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Global attractor for a wave model with nonlocal nonlinear dampingJournal of Mathematical Analysis and Applications (IF 1.3) Pub Date : 2021-11-15 , DOI:10.1016/j.jmaa.2021.125818Cong Zhou, Chunyou SunThis paper investigates the well-posedness and long-time dynamics of a wave model with nonlocal nonlinear damping: utt−Δu+σ(‖∇u‖2)g(ut)+f(u)=h(x). For a new exponent p⁎=6γγ+1(≥3), where γ∈[1,5) is the growth index of the nonlinear damping term g(ut), it shows that, as the growth exponent p of the nonlinearity f(u) satisfies 2≤p≤p⁎, the problem is well-posed and has a global attractor in the natural ...
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Inviscid limit for the damped generalized incompressible Navier-Stokes equations on \begin{document}$ \mathbb{T}^2 $\end{document}Discrete and Continuous Dynamical Systems-Series S (IF 1.8) Pub Date : 2021-10-18 , DOI:10.3934/dcdss.2021124Yang Liu, Chunyou Sun
In this paper, for the damped generalized incompressible Navier-Stokes equations on $ \mathbb{T}^{2} $ as the index $ \alpha $ of the general dissipative operator $ (-\Delta)^{\alpha} $ belongs to $ (0,\frac{1}{2}] $, we prove the absence of anomalous dissipation of the long time averages of entropy. We also give a note to show that, by using the $ L^{\infty} $ bounds given in Caffarelli et al. [4]
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Inertial manifolds for a singularly non-autonomous semi-linear parabolic equationsProceedings of the American Mathematical Society (IF 1.0) Pub Date : 2021-09-21 , DOI:10.1090/proc/15606Xinhua Li, Chunyou SunAbstract:This paper devotes to the existence of an $N$-dimensional inertial manifold for a class of singularly, i.e. $A(t)$ may degenerate to $0$ at some time $t$, non-autonomous parabolic equations \begin{equation*} \partial _{t}u+A(t)u=F(t,u)+g(x,t),\;t>\tau ;\; \; u|_{t=\tau }=u_{\tau }(x),\;x\in \Omega , \end{equation*} where $A(t)\geq 0$ for any $t\geq \tau$, and $\Omega \subset \mathbb {R}^{d}$ ...
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Pullback attractors for 2D MHD equations on time-varying domainsDiscrete and Continuous Dynamical Systems-Series A (IF 1.1) Pub Date : 2021-09-16 , DOI:10.3934/dcds.2021132Daomin Cao, Xiaoya Song, Chunyou Sun
In the present paper, we consider the asymptotic dynamics of 2D MHD equations defined on the time-varying domains with homogeneous Dirichlet boundary conditions. First we introduce some coordinate transformations to construct the invariance of the divergence operators in any $ n $-dimensional spaces and establish some equivalent estimates of the vectors between the time-varying domains and the cylindrical
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Pullback attractors for a critical degenerate wave equation with time-dependent dampingNonlinear Analysis: Real World Applications (IF 2.0) Pub Date : 2021-09-15 , DOI:10.1016/j.nonrwa.2021.103421Dandan Li, Qingquan Chang, Chunyou Sun
The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term ∂ttu+β(t)∂tu=Lu(x,t)+f(u) on a bounded domain Ω⊂RN with Dirichlet boundary conditions. Under some restrictions on β(t) and critical growth restrictions on the nonlinear term f, we will prove the local and global well-posedness of the solution and derive
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Reaction-diffusion systems with supercritical nonlinearities revisitedMathematische Annalen (IF 1.4) Pub Date : 2021-06-22 , DOI:10.1007/s00208-021-02222-6Anna Kostianko, Chunyou Sun, Sergey Zelik
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the main attention to the supercritical case, where the nonlinearity is not subordinated to the linear part of the equation trying to put as small as possible amount of
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Infinite energy solutions for weakly damped quintic wave equations in $\mathbb {R}^3$Transactions of the American Mathematical Society (IF 1.3) Pub Date : 2020-12-23 , DOI:10.1090/tran/8317Xinyu Mei, Anton Savostianov, Chunyou Sun, Sergey Zelik
The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global well-posedness of the so-called Shatah-Struwe solutions, their dissipativity, the existence of a locally compact global attractors (in the uniformly local phase spaces) and their extra regularity
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Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearityDiscrete and Continuous Dynamical Systems-Series A (IF 1.1) Pub Date : 2020-07-03 , DOI:10.3934/dcds.2020270Xinyu Mei, Yangmin Xiong, Chunyou Sun
In this paper, the non-autonomous dynamical behavior of weakly damped wave equation with a sup-cubic nonlinearity is considered in locally uniform spaces. We first prove the global well-posedness of the Shatah-Struwe solutions, then establish the existence of the $ \big(H_{lu}^{1}(\mathbb{R}^{3})\times L_{lu}^{2}(\mathbb{R}^{3}),H_{\rho}^{1}(\mathbb{R}^{3})\times L_{\rho}^{2}(\mathbb{R}^{3})\big) $-pullback
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An optimal nearly analytic splitting method for solving 2D acoustic wave equationsJournal of Applied Geophysics Pub Date : 2020-06-01 , DOI:10.1016/j.jappgeo.2020.104029Nam Yun, Chun-You Sun, Chol SimAbstract In this article, we suggest a new optimal nearly analytic splitting (ONAS) method for 2D acoustic wave simulation. We first split 2D acoustic wave equation into the local one-dimensional (LOD) equations. Then we solve each of these equations over half of the time step used for the complete 2D wave equation using technique similar to the optimal nearly analytic discrete method (ONADM) for the ...
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Inertial manifolds for the 3D modified-Leray-α modelJournal of Differential Equations (IF 2.4) Pub Date : 2020-02-01 , DOI:10.1016/j.jde.2019.09.001Xinhua Li, Chunyou SunAbstract In this paper, we investigate the critical modified-Leray-α model in T 3 and prove the existence of an N-dimensional inertial manifold for this problem. ...
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Asymptotic dynamics of non-autonomous fractional reaction-diffusion equations on bounded domainsTopological Methods in Nonlinear Analysis Pub Date : 2020-01-19 , DOI:10.12775/tmna.2019.063Xin Li, Wenxian Shen, Chunyou SunIn this paper, we consider the asymptotic dynamics of non-autonomous fractional reaction-diffusion equations of the form \[u_{t}+(-\Delta)^{s}u+f(u)=g(t)\] complemented with the Dirichlet boundary condition on a bounded domain. First, we obtain some higher-attraction results for pullback attractors, that is, without any additional $t$-differentiability assumption on the forcing term $g$, for any space ...
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A nearly analytic symplectic partitioned Runge–Kutta method based on a locally one‐dimensional technique for solving two‐dimensional acoustic wave equationsGeophysical Prospecting (IF 2.6) Pub Date : 2020-01-13 , DOI:10.1111/1365-2478.12924Chol Sim, Chunyou Sun, Nam YunIn this paper, we develop a new nearly analytic symplectic partitioned Runge–Kutta method based on locally one‐dimensional technique for numerically solving two‐dimensional acoustic wave equations. We first split two‐dimensional acoustic wave equation into the local one‐dimensional equations and transform each of the split equations into a Hamiltonian system. Then, we use both a nearly analytic discrete ...
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Long-time behavior for a class of weighted equations with degeneracyDiscrete and Continuous Dynamical Systems-Series A (IF 1.1) Pub Date : 2020-01-01 , DOI:10.3934/dcds.2020098Shan Ma,Chunyou Sun
In this paper we study the existence and some properties of the global attractors for a class of weighted equations when the weighted Sobolev space \begin{document}$ H_0^{1,a}(\Omega) $\end{document} (see Definition 1.1) cannot be bounded embedded into \begin{document}$ L^2(\Omega) $\end{document} . We claim that the dimension of the global attractor is infinite by estimating its lower bound of \begin{document}$
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Random attractors for stochastic time-dependent damped wave equation with critical exponentsDiscrete and Continuous Dynamical Systems-Series B (IF 1.2) Pub Date : 2020-01-01 , DOI:10.3934/dcdsb.2020033Qingquan Chang,Dandan Li,Chunyou Sun
We study the asymptotic behavior of solutions of a stochastic time-dependent damped wave equation. With the critical growth restrictions on the nonlinearity \begin{document}$ f $\end{document} and the time-dependent damped term, we prove the global existence of solutions and characterize their long-time behavior. We show the existence of random attractors with finite fractal dimension in \begin{document}$
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Sigma-subdifferential and its application to minimization problemPositivity (IF 1.0) Pub Date : 2019-07-13 , DOI:10.1007/s11117-019-00693-1Hui Huang, Chunyou SunIn this paper, we study \(\sigma \)-subdifferentials of \(\sigma \)-convex functions. Two equivalent conditions for \(\sigma \)-convexity are given. The formula for the \(\sigma \)-subdifferential of a sum of two functions is established. In terms of \(\sigma \)-subdifferential and Clarke’s normal cone, some Fermat’s rules for minimization problems are obtained. ...
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Dynamics for a stochastic degenerate parabolic equationComputers & Mathematics with Applications (IF 2.9) Pub Date : 2019-05-01 , DOI:10.1016/j.camwa.2018.12.023Qingquan Chang,Dandan Li,Chunyou SunAbstract In this paper we consider the long-time behavior of a class of stochastic degenerate parabolic equations involving an operator which is X -elliptic with respect to a family of locally Lipschitz continuous vector fields X = { X 1 , X 2 , … , X m ˜ } . The nonlinearity satisfies a dissipative condition with polynomial growth of arbitrary order p ≥ 2 . The existence of the random attractor in ...
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