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
A two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics with two pieces of constant states separated by a circular ring is considered. By using the generalized characteristic method and ...A two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics with two pieces of constant states separated by a circular ring is considered. By using the generalized characteristic method and the generalized Rankine-Hugoniot relation, which is a system of ordinary equations, the global solution which includes delta-shock waves and vacuum is constructed.展开更多
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.
基金the National Natural Science Foundation of China(No.10671120)
文摘A two-dimensional non-selfsimilar initial value problem for adhesion particle dynamics with two pieces of constant states separated by a circular ring is considered. By using the generalized characteristic method and the generalized Rankine-Hugoniot relation, which is a system of ordinary equations, the global solution which includes delta-shock waves and vacuum is constructed.
