In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
In this paper, we investigate the finite dimensions of the global attractor for nonlinear higher-order coupled Kirchhoff type equations with strong linear damping in Hilbert spaces E0?and E1. Under the appropriate ass...In this paper, we investigate the finite dimensions of the global attractor for nonlinear higher-order coupled Kirchhoff type equations with strong linear damping in Hilbert spaces E0?and E1. Under the appropriate assumptions, we acquire a precise estimate of the upper bound for its Hausdorff and Fractal dimensions.展开更多
In this paper, we discuss the existence and uniqueness of global solutions, the existence of the family of global attractors and its dimension estimation for generalized Beam-Kirchhoff equation under initial condition...In this paper, we discuss the existence and uniqueness of global solutions, the existence of the family of global attractors and its dimension estimation for generalized Beam-Kirchhoff equation under initial conditions and boundary conditions, using the previous research results for reference. Firstly, the existence of bounded absorption set is proved by using a prior estimation, then the existence and uniqueness of the global solution of the problem is proved by using the classical Galerkin’s method. Finally, Housdorff dimension and fractal dimension of the family of global attractors are estimated by linear variational method and generalized Sobolev-Lieb-Thirring inequality.展开更多
This paper mainly studies the initial value problems of Kirchhoff-type coupled equations. Firstly, by giving the hypothesis of Kirchhoff stress term , the Galerkin’s method obtains the existence uniqueness of the ove...This paper mainly studies the initial value problems of Kirchhoff-type coupled equations. Firstly, by giving the hypothesis of Kirchhoff stress term , the Galerkin’s method obtains the existence uniqueness of the overall solution of the above problem by using a priori estimates in the spaces of E<sub>0</sub> and E<sub>k</sub>, and secondly, it proves that there is a family of global attractors for the above problem, and finally estimates the Hausdorff dimension and the Fractal dimension of the family of global attractors.展开更多
The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence...The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.展开更多
The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. A...The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated.展开更多
In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equ...In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equation.estimate of fractal dimension of attractor.展开更多
This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fr...This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.展开更多
This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s∈(0,1).We first present some conditions for estimating the boundedness of fractal dimension...This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s∈(0,1).We first present some conditions for estimating the boundedness of fractal dimension of a random invariant set.Then we establish the existence and uniqueness of tempered pullback random attractors.Finally,the finiteness of fractal dimension of the random attractors is proved.展开更多
In this paper,we study the wellness and long time dynamic behavior of the solution of the initial boundary value problem for a class of higher order Kirchhoff equations <img src="Edit_e49f9c34-0a5d-4ef2-828f-b...In this paper,we study the wellness and long time dynamic behavior of the solution of the initial boundary value problem for a class of higher order Kirchhoff equations <img src="Edit_e49f9c34-0a5d-4ef2-828f-ba3f0912bed3.png" alt="" />with strong damping terms. We will properly assume the stress term <i>M(s)</i><span style="position:relative;top:6pt;"><v:shape id="_x0000_i1026" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""></v:imagedata></v:shape></span> and<span style="letter-spacing:-0.2pt;"> nonlinear term g(u<sub>t</sub>)<span style="position:relative;top:6pt;"><v:shape id="_x0000_i1027" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz" o:title=""></v:imagedata></v:shape></span>. First, we can prove the existence and uniqueness of the solution of the equation via a prior estimate and Galerkin’s method, then the existence of the family of global attractor is obtained. At last, we can obtain that the Hausdorff dimension and Fractal dimension of the family of global attractor are finite.</span>展开更多
In this paper,we study the dimension estimate of global attractor for a 3D Brinkman-Forchheimer equation.Based on the differentiability of the semigroup with respect to the initial data,we show that the global attract...In this paper,we study the dimension estimate of global attractor for a 3D Brinkman-Forchheimer equation.Based on the differentiability of the semigroup with respect to the initial data,we show that the global attractor of strong solution of the 3D BrinkmanForchheimer equation has finite Hausdorff and fractal dimensions.展开更多
Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations ...Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations and the priori estimates; Existence of the attractors for the discrete system; Estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors.展开更多
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
文摘In this paper, we investigate the finite dimensions of the global attractor for nonlinear higher-order coupled Kirchhoff type equations with strong linear damping in Hilbert spaces E0?and E1. Under the appropriate assumptions, we acquire a precise estimate of the upper bound for its Hausdorff and Fractal dimensions.
文摘In this paper, we discuss the existence and uniqueness of global solutions, the existence of the family of global attractors and its dimension estimation for generalized Beam-Kirchhoff equation under initial conditions and boundary conditions, using the previous research results for reference. Firstly, the existence of bounded absorption set is proved by using a prior estimation, then the existence and uniqueness of the global solution of the problem is proved by using the classical Galerkin’s method. Finally, Housdorff dimension and fractal dimension of the family of global attractors are estimated by linear variational method and generalized Sobolev-Lieb-Thirring inequality.
文摘This paper mainly studies the initial value problems of Kirchhoff-type coupled equations. Firstly, by giving the hypothesis of Kirchhoff stress term , the Galerkin’s method obtains the existence uniqueness of the overall solution of the above problem by using a priori estimates in the spaces of E<sub>0</sub> and E<sub>k</sub>, and secondly, it proves that there is a family of global attractors for the above problem, and finally estimates the Hausdorff dimension and the Fractal dimension of the family of global attractors.
基金supported by the National Natural Science Foundation of China (No.10871156)the Fund of Xi'an Jiaotong University (No.2009xjtujc30)
文摘The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.
基金Project supported by the Natural Science Foundation of Henan Educational Committee of China(No.2003110005)
文摘The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated.
文摘In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equation.estimate of fractal dimension of attractor.
基金Supported by National Natural Science Foundation of China(Grant Nos.11571245,11771444,11871138 and11871049)funding of V.C.&V.R.Key Lab of Sichuan Province+2 种基金the Yue Qi Young Scholar ProjectChina University of Mining and Technology(Beijing)China Scholarship Council(CSC)。
文摘This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.
基金The authors would like to thank the reviewers for their helpful comments.This work was partially supported by the National Natural Science Foundation of China(11871138)joint research project of Laurent Mathematics Center of Sichuan Normal UniversityNational-Local Joint Engineering Laboratory of System Credibility Automatic Verification,funding of V.C.&V.R.Key Lab of Sichuan Province.
文摘This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s∈(0,1).We first present some conditions for estimating the boundedness of fractal dimension of a random invariant set.Then we establish the existence and uniqueness of tempered pullback random attractors.Finally,the finiteness of fractal dimension of the random attractors is proved.
文摘In this paper,we study the wellness and long time dynamic behavior of the solution of the initial boundary value problem for a class of higher order Kirchhoff equations <img src="Edit_e49f9c34-0a5d-4ef2-828f-ba3f0912bed3.png" alt="" />with strong damping terms. We will properly assume the stress term <i>M(s)</i><span style="position:relative;top:6pt;"><v:shape id="_x0000_i1026" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz" o:title=""></v:imagedata></v:shape></span> and<span style="letter-spacing:-0.2pt;"> nonlinear term g(u<sub>t</sub>)<span style="position:relative;top:6pt;"><v:shape id="_x0000_i1027" type="#_x0000_t75" o:ole="" style="width:27pt;height:17.25pt;"><v:imagedata src="file:///C:\Users\TEST~1.SCI\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz" o:title=""></v:imagedata></v:shape></span>. First, we can prove the existence and uniqueness of the solution of the equation via a prior estimate and Galerkin’s method, then the existence of the family of global attractor is obtained. At last, we can obtain that the Hausdorff dimension and Fractal dimension of the family of global attractor are finite.</span>
基金Supported by the National Natural Science Foundation of China(12001420)。
文摘In this paper,we study the dimension estimate of global attractor for a 3D Brinkman-Forchheimer equation.Based on the differentiability of the semigroup with respect to the initial data,we show that the global attractor of strong solution of the 3D BrinkmanForchheimer equation has finite Hausdorff and fractal dimensions.
基金Project supported by the National Natural Science Poundation of China (No. 19861004).
文摘Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations and the priori estimates; Existence of the attractors for the discrete system; Estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors.
