Abstract
The thesis is divided into three parts. It includes a brief introduction of the collision kernel, and the uses of the tools in X. Lu, C. Mouhot, <On measure solutions of the Boltzmann equation, part I: moment production and stability estimates.> to derive the result for a solution of spatially homogeneous Boltzmann equation in Lebesgue p-integrable space with finite initial moment and makes it to be controlled by an exponentially like function as time goes on. And after the conclusion comes along some appendices which make the thesis more clear on its way to the final work.