This paper is a discussion of global solutions to the initial value problems for general- ized Banjamin-Bona-Mahony equations.Some long time behaviors of the solutions are presented with the initial data in some certa...This paper is a discussion of global solutions to the initial value problems for general- ized Banjamin-Bona-Mahony equations.Some long time behaviors of the solutions are presented with the initial data in some certain Sobolev spaces.We employ the method of integral estimate, Fourier transform and Gronwall’s inequality.展开更多
The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a pri...The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a priori estimates with the aid of eommu- tator estimate, we apply the Galerkin method to prove the existence of weak solution in the case of periodic domain. Meanwhile, the uniqueness is also obtained. Because the results obtained are independent of domain, the existence and uniqueness of the weak solution for Cauchy problem is also true. Finally, we use the Fourier splitting method to prove the decay of weak solution in three cases respectively.展开更多
文摘This paper is a discussion of global solutions to the initial value problems for general- ized Banjamin-Bona-Mahony equations.Some long time behaviors of the solutions are presented with the initial data in some certain Sobolev spaces.We employ the method of integral estimate, Fourier transform and Gronwall’s inequality.
基金Sponsored by the Fundamental Research Funds for the Central Universities(2010QS04)the National Science Foundation of China(11201475,11126160,11201185)Zhejiang Provincial Natural Science Foundation of China under Grant(LQ12A01013)
文摘The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a priori estimates with the aid of eommu- tator estimate, we apply the Galerkin method to prove the existence of weak solution in the case of periodic domain. Meanwhile, the uniqueness is also obtained. Because the results obtained are independent of domain, the existence and uniqueness of the weak solution for Cauchy problem is also true. Finally, we use the Fourier splitting method to prove the decay of weak solution in three cases respectively.
