摘要
We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna ＆ Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem.
We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna ＆ Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem.
基金
supported by NSFC(10271121)
the Scientific Research Foundation for the Returned Overseas Chinese Scholars,the Education Ministry of China
sponsored by joint grants of NSFC 10511120278/10611120371
RFBR 04-02-39026
supported by NSFC (10671130)
E-Institutes of Shanghai Municipal Education Commission (E03004)
Shanghai Science and Technology Commission (06JC14092)
Shuguang Project of Shanghai Municipal Education Commission (06SG45)
