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 is devoted to the long time behavior for the Drift-diffusion semiconductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants ...This paper is devoted to the long time behavior for the Drift-diffusion semiconductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) denned by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given.展开更多
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.
基金This work is supported by the Funds of the Nature Science Research of Henan(10371111).
文摘This paper is devoted to the long time behavior for the Drift-diffusion semiconductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) denned by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given.
