A Boltzmann type equation is considered where both, the physical and the velocity space, are bounded. It is assumed that the boundary conditions consist of a reflective as well as a diffusive component. Existence of positive bounds from below and above has been proved. It has been demonstrated that under conditions on the shape of the boundary, the underlying Knudsen type transport semigroup can be embedded in a not necessarily positive group for time t ∈ ℝ. As a consequence, the Boltzmann type equation considered has a unique global solution for time t ∈ [τ ₀, ∞) for some τ ₀ < 0. The time τ ₀ does not depend on the initial value at time 0. It can be arbitrarily small depending on the intensity of the collisions.

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玻尔兹曼方程和努森群 - 边界形状和边界条件

考虑玻尔兹曼型方程，其中物理空间和速度空间都有界。假设边界条件由反射分量和漫射分量组成。已证明存在来自下方和上方的正界。已经证明，在边界形状的条件下，底层的努森型输运半群可以嵌入到时间上不一定为正的群中tε ℝ。因此，所考虑的玻尔兹曼型方程具有唯一的时间全局解tε [τ ₀ ,无穷大） 对于一些τ ₀ < 0。时间τ ₀不依赖于时间 0 处的初始值。它可以任意小，具体取决于碰撞的强度。