论文标题
$ \ mathbb {r} $和相关的boltzmann类型方程式的Knudsen类型组
Knudsen Type Group for Time in $\mathbb{R}$ and Related Boltzmann Type Equations
论文作者
论文摘要
我们考虑在两者的存在下，反射性和扩散边界条件下的有界物理和有限速度空间上的某些玻尔兹曼类型方程。我们介绍了物理空间的形状以及边界条件中反射性和扩散部分之间的关系，以便可以将关联的Knudsen型Semigroup扩展到\ Mathbb {R} $的时间$ t \。此外，我们提供的条件在其下是为时间$ t \ ge 0 $的Boltzmann类型方程式提供的独特全局解决方案，或者在[τ_0，\ infty）$ in $ t $ t \ in [τ_0，\ infty）$中$ t $τ_0<0 <0 $，它与时间0的初始值无关。
We consider certain Boltzmann type equations on a bounded physical and a bounded velocity space under the presence of both, reflective as well as diffusive boundary conditions. We introduce conditions on the shape of the physical space and on the relation between the reflective and the diffusive part in the boundary conditions such that the associated Knudsen type semigroup can be extended to time $t\in\mathbb{R}$. Furthermore, we provide conditions under which there exists a unique global solution to a Boltzmann type equation for time $t\ge 0$ or for time $t\in [τ_0,\infty)$ for some $τ_0<0$ which is independent of the initial value at time 0. Depending on the collision kernel, $τ_0$ can be arbitrarily small.
