We study the singularity formation of smooth solutions for Cauchy problem of the Aw-Rascle traffic model with relaxation.Under the subcharacteristic assumption and general law of the velocity deviation,we construct a ...We study the singularity formation of smooth solutions for Cauchy problem of the Aw-Rascle traffic model with relaxation.Under the subcharacteristic assumption and general law of the velocity deviation,we construct a set of large initial data,and prove that the corresponding smooth solutions blow up in a finite time,and form a cusp singularity in the direction of genuinely nonlinear characteristic.Moreover,under the generic nondegenerate condition on initial data,we give precise description on the blowup time and location.展开更多
基金Min Ding's research was supported by the NSFC(12371226)the Natural Science Foundation of Hubei province(2021CFB452)the Fundamental Research Funds for the Central Universities(104972025KFYjc0092).
文摘We study the singularity formation of smooth solutions for Cauchy problem of the Aw-Rascle traffic model with relaxation.Under the subcharacteristic assumption and general law of the velocity deviation,we construct a set of large initial data,and prove that the corresponding smooth solutions blow up in a finite time,and form a cusp singularity in the direction of genuinely nonlinear characteristic.Moreover,under the generic nondegenerate condition on initial data,we give precise description on the blowup time and location.
