报告题目：Spectral gap can form in soft potentials
报 告 人：段仁军（香港中文大学）
报告时间：2022年11月15日 15:00开始
报告地点：腾讯会议（会议号：765 304 029）
报告摘要：In the talk I will consider the spectral gap for the linearized Boltzmann or Landau equation with soft potentials. It is known that the corresponding collision operators admit only the degenerated spectral gap. We rather prove the formation of spectral gap in the spatially inhomogeneous setting where the space domain is bounded with an inflow boundary condition. The key strategy is to introduce a new Hilbert space with an exponential weight function that involves the inner product of space and velocity variables and also has the strictly positive upper and lower bounds. The action of the transport operator on such space-velocity dependent weight function induces an extra non-degenerate relaxation dissipation in large velocity that can be employed to compensate the degenerate spectral gap and hence give the exponential decay for solutions in contrast with the sub-exponential decay in either the spatially homogeneous case or the case of torus domain. Joint work with Dingqun Deng (Tsinghua University).
报告人简介： 段仁军，香港中文大学教授。2008年在香港城市大学获理学博士学位；2008年至2010年在奥地利科学院作博士后研究；2010年入职香港中文大学。曾获钟家庆数学奖等，长期从事非线性偏微分方程的研究，特别在玻尔兹曼方程和耗散性偏微分方程的研究中作出了有重要意义的工作，成果发表在国际上重要杂志如：CPAM, Trans. AMS, Comm. PDE, ARMA, CMP, Adv Math, M3AS, SIAM JMA, 并在国际上产生了重要的影响。
