where U and F are the vector-valued functions which are defined on R<sup>+</sup>×R<sup>N</sup> and R<sup>+</sup>×R<sup>N</sup>×R<sup>N</sup>,r...where U and F are the vector-valued functions which are defined on R<sup>+</sup>×R<sup>N</sup> and R<sup>+</sup>×R<sup>N</sup>×R<sup>N</sup>,respectively, U=（u<sub>1</sub>,…,u<sub>N</sub>）, F=（f<sub>1</sub>,…,f<sub>N</sub>）, =（<sub>x</sub><sub>1</sub>,……,<sub>x</sub>）<sub>N</sub>. Moreover, F is smooth enough, andits derivatives of all orders are boundary on R×K. K is any compact set in R<sup>2N</sup>.Obviously,展开更多
Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variabl...Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.展开更多
基金Project supported by the Tianyuan Foundation of China.
文摘where U and F are the vector-valued functions which are defined on R<sup>+</sup>×R<sup>N</sup> and R<sup>+</sup>×R<sup>N</sup>×R<sup>N</sup>,respectively, U=（u<sub>1</sub>,…,u<sub>N</sub>）, F=（f<sub>1</sub>,…,f<sub>N</sub>）, =（<sub>x</sub><sub>1</sub>,……,<sub>x</sub>）<sub>N</sub>. Moreover, F is smooth enough, andits derivatives of all orders are boundary on R×K. K is any compact set in R<sup>2N</sup>.Obviously,
文摘Boltzmann equation is an equation which is related to the three variables of x, v, t. In this paper, we mainly study the space-uniform Boltzmann equation which unknown function F is not related to the position variable x. We mainly use the contraction mapping theorem to find the existence of the solution, so our mainly work is to prove the self-mapping, i.e. to prove its uniformly bounded, and then to prove the contraction mapping. There we can get the range of ||B(θ)||L1(L∞), next we can figure out the range of M and T from the conditions what we know. Finally, from these conditions, we can find the existence of the solution.
