报告人：段仁军（香港中文大学）

邀请人：雷远杰

报告时间：2021年12月20日（星期一）14:30-16:30

报告地点：腾讯会议ID：588 577 058

报告题目：On smooth self-similar solutions of the Boltzmann equation with deformation

报告摘要： This talk concerns a modified spatially homogeneous Boltzmann equation with a linear deformation force described by a constant matrix. We construct the smooth self-similar solution with an exponentially growing internal energy via a perturbation approach when the deformation strength is sufficiently small. The particle interaction under consideration includes both the Maxwell molecule and general hard potentials with angular cutoff. Moreover, we also establish the long time asymptotics toward self-similar solutions for the Cauchy problem on the corresponding spatially inhomogeneous equation in torus, which in turn gives the non-negativity of self-similar profiles. It is joint work with Shuangqian Liu.

报告人简介：段仁军，香港中文大学数学系教授，段仁军教授是我国知名的青年数学家。段仁军教授长期从事非线性偏微分方程的研究，特别是在玻尔兹曼方程和耗散性偏微分方程的研究中作出了重要意义的工作，成果发表在在国际上重要杂志如：Communications on Pure and Applied Mathematics、Archive for Rational Mechanics and Analysis、Advances in Mathematics，Communications in Mathematical Physics、Journal of Functional Analysis、Communications in Partial Differential Equations、 Mathematical Models and Methods in Applied Sciences、SIAM Journal on Mathematical Analysis等著名期刊杂志上，并在国际上产生了重要的影响。目前担任Discrete & Continuous Dynamical Systems-B和Nonlinear Analysis: Real World Applications 的编委。