Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied. We propose a new differential variational principle, called the Pfaff-Birkhoff-d＇Alembert principle of...Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied. We propose a new differential variational principle, called the Pfaff-Birkhoff-d＇Alembert principle of Herglotz type. Birkhoff＇s equations for both the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are obtained. According to the relationship between the isochronal variation and the nonisochronal variation, the conditions of the invariance for the Pfaff-Birkhoff-d＇Alembert principle of Herglotz type are given. Then, the conserved quantities for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are deduced. Furthermore, the inverse theorems of the conservation theorems are also established.展开更多
In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial dat...In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial data can be unbounded.Although the existence and uniqueness of the weak entropy solution are obtained,little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation.So we construct such scheme in our paper and get some new results.展开更多
We define a class of geometric flows on a complete Kahler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equa- tions, derivative nonlinear Sc...We define a class of geometric flows on a complete Kahler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equa- tions, derivative nonlinear SchrSdinger equations etc. Furthermore, we consider the existence for these flows from S1 into a complete Kahler manifold and prove some local and global existence results.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(Grant No.KYZZ16-0479)the Innovation Program for Postgraduate of Suzhou University of Science and Technology,China(Grant No.SKCX16-058)
文摘Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied. We propose a new differential variational principle, called the Pfaff-Birkhoff-d＇Alembert principle of Herglotz type. Birkhoff＇s equations for both the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are obtained. According to the relationship between the isochronal variation and the nonisochronal variation, the conditions of the invariance for the Pfaff-Birkhoff-d＇Alembert principle of Herglotz type are given. Then, the conserved quantities for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are deduced. Furthermore, the inverse theorems of the conservation theorems are also established.
文摘In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{ tu ＋ xf（u） ＋ yg（u） = 0,u（x,y,0） = u0（x,y）.In which initial data can be unbounded.Although the existence and uniqueness of the weak entropy solution are obtained,little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation.So we construct such scheme in our paper and get some new results.
基金Supported by National Natural Science Foundation of China(Grant No.10990013)
文摘We define a class of geometric flows on a complete Kahler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equa- tions, derivative nonlinear SchrSdinger equations etc. Furthermore, we consider the existence for these flows from S1 into a complete Kahler manifold and prove some local and global existence results.
