学术报告（王海涛 2024.10.30）

摘要：Mixture Lemma plays a fundamental role in the construction of Green's function for Boltzmann equation. It reveals that the mixture of transport and collision (gain term) will transfer the microscopic velocity regularity to macroscopic space regularity. In this talk, we will introduce two generalizations of this lemma. The first one shows that the mixture not only transfers regularity, but also creates regularity and decay as many as one desires. The second one constructs the mixture mechanism for fractional derivative. Their applications will also be discussed.