Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H^1 （Ω, C ×R） by using ...Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H^1 （Ω, C ×R） by using Galerkin method. Secondly, by using an iteration procedure, regularity estimates for the linear semigroups, it is proved that the model for liquid mixture of 3He-4He has a unique solution in H^k（Ω, C × R） for all k ≥ 1.展开更多
In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded doma...In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k（Ω） in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k ∈ [0, 1] to the case k∈ [0, ∞）.展开更多
Properties for tensor products of semigroups are considered and the solutions of the equationAC - CB = Q are discussed. Results obtained in this paper considerably generalize thoseobtained in [9].
In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means o...In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.展开更多
In this paper,we derive a time-dependent Ginzburg-Landau model for liquid^(4)He coupling with an applied magnetic field basing on the Le Chatlier principle.We also obtain the existence and uniqueness of global weak so...In this paper,we derive a time-dependent Ginzburg-Landau model for liquid^(4)He coupling with an applied magnetic field basing on the Le Chatlier principle.We also obtain the existence and uniqueness of global weak solution for this model.In addition,by utilizing the regularity estimates for linear semigroup,we prove that the model possesses a global classical solution.展开更多
The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the ...The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the approximate controllability of the bilinear control problem is equivalent to the approximate controllability of a discrete problem, using the method developed by Loreti and Siconolfi to approximate the bilinear control problem in an infinite-dimensional Banach space by means of a sequence of discrete problems. Finally, the necessary conditions for the bilinear system to be approximately controllable are stste and proved.展开更多
基金Sponsored by the National Natural Science Foundation of China(11071177)NSF of Sichuan Science and Technology Department of China(2010JY0057)the NSF of Sichuan Education Department of China(11ZA102)
文摘Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper. First, it is proved that this system possesses a unique global weak solution in H^1 （Ω, C ×R） by using Galerkin method. Secondly, by using an iteration procedure, regularity estimates for the linear semigroups, it is proved that the model for liquid mixture of 3He-4He has a unique solution in H^k（Ω, C × R） for all k ≥ 1.
文摘In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k（Ω） in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k ∈ [0, 1] to the case k∈ [0, ∞）.
文摘Properties for tensor products of semigroups are considered and the solutions of the equationAC - CB = Q are discussed. Results obtained in this paper considerably generalize thoseobtained in [9].
基金Supported by the NSF of China (Nos. 10571142, 10771167)
文摘In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.
基金supported by the National Natural Science Foundation of China(Nos.11771306,11901408)。
文摘In this paper,we derive a time-dependent Ginzburg-Landau model for liquid^(4)He coupling with an applied magnetic field basing on the Le Chatlier principle.We also obtain the existence and uniqueness of global weak solution for this model.In addition,by utilizing the regularity estimates for linear semigroup,we prove that the model possesses a global classical solution.
文摘The aim of this paper is to study approximate controllability for bilinear systems in the general case. The existence and uniqueness of solutions to bilinear evolution equations are obtained. The paper shows that the approximate controllability of the bilinear control problem is equivalent to the approximate controllability of a discrete problem, using the method developed by Loreti and Siconolfi to approximate the bilinear control problem in an infinite-dimensional Banach space by means of a sequence of discrete problems. Finally, the necessary conditions for the bilinear system to be approximately controllable are stste and proved.
