The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions （2000）. The aim of this paper is to discuss the Cauchy...The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions （2000）. The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the formδtfi＋（fi^mi）=Qi（f1,f2...,fn）,（mi〉1,i-1,...n）with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.展开更多
The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion th...The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion that one\|dimensional Broadwell model cannot have multi\|dimensional similarity solutions is proved and the proof is simplified.展开更多
The Broadwell model is the simplest spatial model of the Boltzmann equation. The exact travelling wave solutions of the Broadwell model are studied in a concise way with proof of their existence and uniqueness of form...The Broadwell model is the simplest spatial model of the Boltzmann equation. The exact travelling wave solutions of the Broadwell model are studied in a concise way with proof of their existence and uniqueness of form. The results ameliorate the conclusions of previous investigator. The results suggest a general method for obtaining nontrivial exact solutions for the similar discrete Boltzmann equation.展开更多
文摘The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions （2000）. The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the formδtfi＋（fi^mi）=Qi（f1,f2...,fn）,（mi〉1,i-1,...n）with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.
基金Supported by National Natural Science Foundation ofChina(No. 196 310 6 0 ) and Post Doctor Science Foun-dation of China
文摘The exact (1+1)\|dimensional similarity solutions of the Broadwell model are studied in a concise way. A new type of exact (1+1)\|dimensional similarity solutions of the Broadwell model are obtained. The conclusion that one\|dimensional Broadwell model cannot have multi\|dimensional similarity solutions is proved and the proof is simplified.
基金Supported by the National Natural Science Foundationof China(No.196 310 6 0 )
文摘The Broadwell model is the simplest spatial model of the Boltzmann equation. The exact travelling wave solutions of the Broadwell model are studied in a concise way with proof of their existence and uniqueness of form. The results ameliorate the conclusions of previous investigator. The results suggest a general method for obtaining nontrivial exact solutions for the similar discrete Boltzmann equation.
