The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.An interesting result is also obtain...The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.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
This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-sca...This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chem- ical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.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
In this paper we prove the existence of global attractor for the generalized dissipative KdVequation on R, and give an upper bound for its Hausdorff and fractal dimensions.
Fractals are essentially characterized by their self-similarity at different scales and non-integer Hausdorff dimensions[1],while crystals always show certain symmetries and discrete diffraction diagrams[2].Thus,a fra...Fractals are essentially characterized by their self-similarity at different scales and non-integer Hausdorff dimensions[1],while crystals always show certain symmetries and discrete diffraction diagrams[2].Thus,a fractal crystal by definition must be identical at all scales with a compatible symmetry with crystals.Although fractals,e.g.snowflakes,trees,coastlines and blood-vascular systems,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
In this paper,the long time behaviors of non-autonomous evolution system describing geophysical flow within the earth are studied.The uniqueness and existence of the solution to the evolution system and the existence ...In this paper,the long time behaviors of non-autonomous evolution system describing geophysical flow within the earth are studied.The uniqueness and existence of the solution to the evolution system and the existence of uniform attractor are proven.Moreover,the upper bounds of the uniform attractor's hausdorff and Fractal dimensions are obtained.展开更多
In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in with finite Hausdorff and fractal dimensions.
基金Supported Partially by the National Natural Science Foundation of China ( 1 0 1 31 0 5 0 ) ,theEducation Ministry of China and Shanghai Science and Technology Committee( 0 3QMH1 40 7)Supported by the National Natural Science Foundation of China( 1 986
文摘The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.
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.
基金supported by the National Natural Science Foundation of China(No.11271141)
文摘This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chem- ical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.
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.
文摘In this paper we prove the existence of global attractor for the generalized dissipative KdVequation on R, and give an upper bound for its Hausdorff and fractal dimensions.
文摘Fractals are essentially characterized by their self-similarity at different scales and non-integer Hausdorff dimensions[1],while crystals always show certain symmetries and discrete diffraction diagrams[2].Thus,a fractal crystal by definition must be identical at all scales with a compatible symmetry with crystals.Although fractals,e.g.snowflakes,trees,coastlines and blood-vascular systems,
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.
基金This research is supported by the Special Funds for Major State Basic Research Projects(G1999032801) by the Natural Science Foundation of China with Grant No.19671067 and 10001028.
文摘In this paper,the long time behaviors of non-autonomous evolution system describing geophysical flow within the earth are studied.The uniqueness and existence of the solution to the evolution system and the existence of uniform attractor are proven.Moreover,the upper bounds of the uniform attractor's hausdorff and Fractal dimensions are obtained.
基金the Scientific Research Foundation for Returned Overseas Chinese Scholars. State Education Commission.
文摘In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in with finite Hausdorff and fractal dimensions.
