论文标题
测量有价值的解决方案，用于与非弹性长距离相互作用的空间均匀的玻尔兹曼方程
Measure Valued Solution to the Spatially Homogeneous Boltzmann Equation with Inelastic Long-Range Interactions
论文作者
论文摘要
本文是研究没有毕业生的角度截止假设的非弹性玻尔兹曼方程，其中在概率度量的概率度量方面为麦克斯韦分子的求解解决方案提供了良好的求解理论，该理论是由cannone-karch在[COMM中定义的概率度量。纯的。应用。数学。 63（2010），747-778]通过傅立叶变换和无限能量解决方案也不是先验的。同时，引入了非弹性碰撞机制的几何关系，以处理非切割碰撞核的强奇异性。此外，我们将自相似的解决方案扩展到Boltzmann方程，并用Bobylev-Cercignani在[J.统计PHY。 106（2002），1039-1071]通过一种建设性方法，这也被证明是借助渐近稳定性的大型渐近稳定解决方案，从某种意义上来说会导致。
This paper is to study the inelastic Boltzmann equation without Grad's angular cutoff assumption, where the well-posedness theory of the solution to the initial value problem is established for the Maxwellian molecules in a space of probability measure defined by Cannone-Karch in [Comm. Pure. Appl. Math. 63 (2010), 747-778] via Fourier transform and the infinite energy solutions are not a priori excluded as well. Meanwhile, the geometric relation of the inelastic collision mechanism is introduced to handle the strong singularity of the non-cutoff collision kernel. Moreover, we extend the self-similar solution to the Boltzmann equation with infinite energy shown by Bobylev-Cercignani in [J. Stat. Phy. 106 (2002), 1039-1071] to the inelastic case by a constructive approach, which is also proved to be the large-time asymptotic steady solution with the help of asymptotic stability result in a certain sense.
