 作 者: ( "chunyou sun" OR "chunyou sun" )

The Journal of Geometric Analysis (IF 1.1) Pub Date : 20230703 , DOI:10.1007/s12220023013533Cong Zhou, Chunyou SunThis paper investigates the wellposedness and stability of the beam model with degenerate nonlocal damping: \( u_{tt}+\Delta ^2uM(\Vert \nabla u\Vert ^2)\Delta u+(\Vert \Delta u\Vert ^\theta +q\Vert u_t\Vert ^\rho )(\Delta )^\delta u_t+f(u)=0\ \ \hbox {in} \ \ \Omega \times {\mathbb {R}}^+,\) where \(\Omega \subset {\mathbb {R}}^n\) is a bounded domain with smooth boundary, \(\theta \ge 1,~q\ge ...

Journal of Geometric Analysis Pub Date : 20230703 , DOI:10.1007/s12220023013533Cong Zhou, Chunyou SunThis paper investigates the wellposedness and stability of the beam model with degenerate nonlocal damping: \( u_{tt}+\Delta ^2uM(\Vert \nabla u\Vert ^2)\Delta u+(\Vert \Delta u\Vert ^\theta +q\Vert u_t\Vert ^\rho )(\Delta )^\delta u_t+f(u)=0\ \ \hbox {in} \ \ \Omega \times {\mathbb {R}}^+,\) where \(\Omega \subset {\mathbb {R}}^n\) is a bounded domain with smooth boundary, \(\theta \ge 1,~q\ge ...

Journal of Evolution Equations (IF 1.4) Pub Date : 20230606 , DOI:10.1007/s0002802300894yChunyou Sun, Bao Quoc Tang, Juan YangWe 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 nonnegativity 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 ...

Applied Mathematics Letters (IF 3.7) Pub Date : 20230406 , 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 timedependent coefficient D(t) goes to infinity as t→∞. The wellposedness and ...

arXiv  MATH  Dynamical Systems Pub Date : 20230306 , DOI:arxiv2303.02991Yangmin Xiong, Chunyou SunThis paper is concerned with a nonautonomous supcubic 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 translationcompact. ...

Stochastics and Dynamics (IF 1.1) Pub Date : 20230203 , DOI:10.1142/s0219493722400366Yangmin Xiong, Xiaoya Song, Chunyou SunThis paper aims at the longtime behavior of nonautonomous 2D Navier–Stokes equations with a class of external forces which are Hvalued measures in time. We first establish the wellposedness of solutions as well as the existence of a strong uniform attractor, and then pay the main attention on the estimation of 𝜀entropy for such uniform attractor in the standard energy phase space. ...

Journal of Mathematical Physics (IF 1.3) Pub Date : 20221017 , DOI:10.1063/5.0063223Jinfang He, Shan Ma, Chunyou Sun, Lu YangIn this article, we study the longtime behavior of solutions of nonautonomous 2D magnetohydrodynamics equations with partial dissipation and timedependent 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 ...

The Journal of Geometric Analysis (IF 1.1) Pub Date : 20220923 , DOI:10.1007/s12220022010258Xiong Liu, Chunyou Sun, Sibei YangLet \(n\ge 2\), \(\Omega \subset {\mathbb {R}}^n\) be a bounded nontangentially 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 ...

Journal of Geometric Analysis Pub Date : 20220923 , DOI:10.1007/s12220022010258Xiong Liu, Chunyou Sun, Sibei YangLet \(n\ge 2\), \(\Omega \subset {\mathbb {R}}^n\) be a bounded nontangentially 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 ...

Journal of Mathematical Physics (IF 1.3) Pub Date : 20220617 , 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 timedependent Darcy flow. Furthermore, stationary statistical solutions of this system are constructed from the global attractor. ...

arXiv  MATH  Analysis of PDEs Pub Date : 20220505 , DOI:arxiv2205.02498Anna Kostianko, Chunyou Sun, Bao Quoc Tang, Juan Yang, Sergey ZelikReactiondiffusion systems with mass dissipation are known to possess blowup 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 ...

Journal of Differential Equations (IF 2.4) Pub Date : 20220228 , DOI:10.1016/j.jde.2022.02.045Jinfang He, Shan Ma, Chunyou SunThis article is devoted to the global wellposedness and the longtime behavior of solutions of a 2D Boussinesq equations with partial dissipation. We prove that this system is global wellposed under some weaker assumptions on the initial data and has a weak sigmaattractor which retains some of the common properties of global attractors for the dissipative dynamical system, moreover, the local attractor ...

SIAM Journal on Mathematical Analysis (IF 2.0) Pub Date : 20220104 , DOI:10.1137/20m1375437Anna Kostianko, Xinhua Li, Chunyou Sun, Sergey ZelikSIAM Journal on Mathematical Analysis, Volume 54, Issue 1, Page 268305, 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 MalletParet. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number ...

Journal of Mathematical Analysis and Applications (IF 1.3) Pub Date : 20211115 , DOI:10.1016/j.jmaa.2021.125818Cong Zhou, Chunyou SunThis paper investigates the wellposedness and longtime 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 wellposed and has a global attractor in the natural ...

Discrete and Continuous Dynamical SystemsSeries S (IF 1.8) Pub Date : 20211018 , DOI:10.3934/dcdss.2021124Yang Liu, Chunyou SunIn this paper, for the damped generalized incompressible NavierStokes 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] ...

Proceedings of the American Mathematical Society (IF 1.0) Pub Date : 20210921 , 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 $t$, nonautonomous 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 $\Omega \subset \mathbb {R}^{d}$ ...

Discrete and Continuous Dynamical SystemsSeries A (IF 1.1) Pub Date : 20210916 , DOI:10.3934/dcds.2021132Daomin Cao, Xiaoya Song, Chunyou SunIn the present paper, we consider the asymptotic dynamics of 2D MHD equations defined on the timevarying 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 timevarying domains and the cylindrical ...

Nonlinear Analysis: Real World Applications (IF 2.0) Pub Date : 20210915 , DOI:10.1016/j.nonrwa.2021.103421Dandan Li, Qingquan Chang, Chunyou SunThe aim of this paper is to analyze the longtime dynamical behavior of the solution for a degenerate wave equation with timedependent 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 wellposedness of the solution and derive ...

Mathematische Annalen (IF 1.4) Pub Date : 20210622 , DOI:10.1007/s00208021022226Anna Kostianko, Chunyou Sun, Sergey ZelikWe give a comprehensive study of the analytic properties and longtime behavior of solutions of a reactiondiffusion 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 ...

Transactions of the American Mathematical Society (IF 1.3) Pub Date : 20201223 , DOI:10.1090/tran/8317Xinyu Mei, Anton Savostianov, Chunyou Sun, Sergey ZelikThe paper gives a comprehensive study of infiniteenergy solutions and their longtime behavior for semilinear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global wellposedness of the socalled ShatahStruwe solutions, their dissipativity, the existence of a locally compact global attractors (in the uniformly local phase spaces) and their extra regularity ...

Discrete and Continuous Dynamical SystemsSeries A (IF 1.1) Pub Date : 20200703 , DOI:10.3934/dcds.2020270Xinyu Mei, Yangmin Xiong, Chunyou SunIn this paper, the nonautonomous dynamical behavior of weakly damped wave equation with a supcubic nonlinearity is considered in locally uniform spaces. We first prove the global wellposedness of the ShatahStruwe 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 ...

Journal of Applied Geophysics Pub Date : 20200601 , DOI:10.1016/j.jappgeo.2020.104029Nam Yun, ChunYou 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 onedimensional (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 ...

Journal of Differential Equations (IF 2.4) Pub Date : 20200201 , DOI:10.1016/j.jde.2019.09.001Xinhua Li, Chunyou SunAbstract In this paper, we investigate the critical modifiedLerayα model in T 3 and prove the existence of an Ndimensional inertial manifold for this problem. ...

Topological Methods in Nonlinear Analysis Pub Date : 20200119 , DOI:10.12775/tmna.2019.063Xin Li, Wenxian Shen, Chunyou SunIn this paper, we consider the asymptotic dynamics of nonautonomous fractional reactiondiffusion 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 higherattraction results for pullback attractors, that is, without any additional $t$differentiability assumption on the forcing term $g$, for any space ...

Geophysical Prospecting (IF 2.6) Pub Date : 20200113 , DOI:10.1111/13652478.12924Chol 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 ...

Discrete and Continuous Dynamical SystemsSeries A (IF 1.1) Pub Date : 20200101 , DOI:10.3934/dcds.2020098Shan Ma,Chunyou SunIn 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) $\end{document} . We claim that the dimension of the global attractor is infinite by estimating its lower bound of \begin{document}$ ...

Discrete and Continuous Dynamical SystemsSeries B (IF 1.2) Pub Date : 20200101 , DOI:10.3934/dcdsb.2020033Qingquan Chang,Dandan Li,Chunyou SunWe study the asymptotic behavior of solutions of a stochastic timedependent damped wave equation. With the critical growth restrictions on the nonlinearity \begin{document}$ f $\end{document} and the timedependent damped term, we prove the global existence of solutions and characterize their longtime behavior. We show the existence of random attractors with finite fractal dimension in \begin{document}$ ...


Positivity (IF 1.0) Pub Date : 20190713 , DOI:10.1007/s11117019006931Hui 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. ...

Computers & Mathematics with Applications (IF 2.9) Pub Date : 20190501 , DOI:10.1016/j.camwa.2018.12.023Qingquan Chang,Dandan Li,Chunyou SunAbstract In this paper we consider the longtime 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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