In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcatio...In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcation problem with parameter symmetry factors through another is given. The corresponding results in [1]-[6] are generalized.展开更多
The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, t...The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.展开更多
The Green form N(z, w) of (0, 1 )-forms with respect to the harmonic operator in theinvariant metric of a ball B^n in C^n is constructed. It is proved that for any differen-tiable (0, 1)-form g(z) in B^n with compact ...The Green form N(z, w) of (0, 1 )-forms with respect to the harmonic operator in theinvariant metric of a ball B^n in C^n is constructed. It is proved that for any differen-tiable (0, 1)-form g(z) in B^n with compact support and ?g = 0, the functionis a solution of the ?-equation ?v = g such that v vanishes on the boundary ?B^n of B^n.展开更多
The Brio system is a 2 × 2 fully nonlinear system of conservation laws which arises as a simplified model in the study of plasmas. The present paper offers explicit solutions to this system subjected to initial c...The Brio system is a 2 × 2 fully nonlinear system of conservation laws which arises as a simplified model in the study of plasmas. The present paper offers explicit solutions to this system subjected to initial conditions containing Dirac masses. The concept of a solution emerges within the framework of a distributional product and represents a consistent extension of the concept of a classical solution. Among other features, the result shows that the space of measures is not sufficient to contain all solutions of this problem.展开更多
基金This work is supported by NNSF of China(10271023) and Hunan Provincial Natural Science Foundation of China(04JJ3072).
文摘In this paper versal unfolding theorem of multiparameter equivariant bifurcation problem with parameter symmetry is given. The necessary and sufficient condition that unfolding of multiparameter equivariant bifurcation problem with parameter symmetry factors through another is given. The corresponding results in [1]-[6] are generalized.
基金Project supported by the National Natural Science Foundation of China(No.11371240)the Scientific Research Innovation Project of Shanghai Municipal Education Commission(No.11ZZ84)the grant of "The First-Class Discipline of Universities in Shanghai"
文摘The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.
文摘The Green form N(z, w) of (0, 1 )-forms with respect to the harmonic operator in theinvariant metric of a ball B^n in C^n is constructed. It is proved that for any differen-tiable (0, 1)-form g(z) in B^n with compact support and ?g = 0, the functionis a solution of the ?-equation ?v = g such that v vanishes on the boundary ?B^n of B^n.
文摘The Brio system is a 2 × 2 fully nonlinear system of conservation laws which arises as a simplified model in the study of plasmas. The present paper offers explicit solutions to this system subjected to initial conditions containing Dirac masses. The concept of a solution emerges within the framework of a distributional product and represents a consistent extension of the concept of a classical solution. Among other features, the result shows that the space of measures is not sufficient to contain all solutions of this problem.
