This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn i...This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.展开更多
The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for ...The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for the attractor under Neumann boundary condition. Next, the same problem is discussed for reaction diffusion system with uniformly contracting rectangle, and it reveals that the maximal attractor of classical solution for such system in the whole space is only necessary to be established in some invariant region. Finally, a few examples of application are given.展开更多
On the basis of the existence of the maximal attractor of the m-dimensional Cahn-Hilliard system in the product spaces （L2（Ω））^m and （H2（Ω））^m, in this paper, its Hausdorff dimension is estimated by calculat...On the basis of the existence of the maximal attractor of the m-dimensional Cahn-Hilliard system in the product spaces （L2（Ω））^m and （H2（Ω））^m, in this paper, its Hausdorff dimension is estimated by calculating the orthogonal projection of the linear variational operator of the system.展开更多
In this paper we discuss maximal attractors of the m-dimensional Cahn-Hilliard System in the product spaces (L 2(?)) m and (H 2(?)) m in terms of D. Henry’s general theory and from the viewpoint of compactness and ab...In this paper we discuss maximal attractors of the m-dimensional Cahn-Hilliard System in the product spaces (L 2(?)) m and (H 2(?)) m in terms of D. Henry’s general theory and from the viewpoint of compactness and absorptivity of semigroups as R. Temam did. After giving the existence and uniqueness of global solutions, we technically restrict our discussion to some subspaces, give estimates with a new graph norm, and obtain the existence of maximal attractors and some properties of them.展开更多
A fully discrete finite difference scheme for dissipative Klein-Gordon-SchrSdinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solut...A fully discrete finite difference scheme for dissipative Klein-Gordon-SchrSdinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding the- orems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in H2 × H2 ×H1 over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.展开更多
基金supported in part by the NSF of China (10571024,10871040)the grant of Prominent Youth of Henan Province of China (0412000100)
文摘This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.
基金This work is supported by the Natural Science Foundation of China(10071048) Excellent Young Teachers Program by the MOE of China
文摘The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for the attractor under Neumann boundary condition. Next, the same problem is discussed for reaction diffusion system with uniformly contracting rectangle, and it reveals that the maximal attractor of classical solution for such system in the whole space is only necessary to be established in some invariant region. Finally, a few examples of application are given.
基金NSFC (China) grants # 10171101 and # 10428104 TRAPOYTChina MOE Doctoral Base Research Grant
文摘On the basis of the existence of the maximal attractor of the m-dimensional Cahn-Hilliard system in the product spaces （L2（Ω））^m and （H2（Ω））^m, in this paper, its Hausdorff dimension is estimated by calculating the orthogonal projection of the linear variational operator of the system.
基金Supported by NNSFC(China) Grant#10171071China Education Ministry Research Grants
文摘In this paper we discuss maximal attractors of the m-dimensional Cahn-Hilliard System in the product spaces (L 2(?)) m and (H 2(?)) m in terms of D. Henry’s general theory and from the viewpoint of compactness and absorptivity of semigroups as R. Temam did. After giving the existence and uniqueness of global solutions, we technically restrict our discussion to some subspaces, give estimates with a new graph norm, and obtain the existence of maximal attractors and some properties of them.
基金supported by the National Natural Science Foundation of China(No.10371077)
文摘A fully discrete finite difference scheme for dissipative Klein-Gordon-SchrSdinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding the- orems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in H2 × H2 ×H1 over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.
