• 日時：2019年11月1日（金） 16:30-17:30
• 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 111講義室（キャンパスマップ 53番）
• 講師：Prof. Francesco Salvarani (Dipartimento di Matematica, Università di Pavia, Italy)
• 題目：On the homogenization problem for the linear Boltzmann equation
• 要旨：In this talk, we study the homogenization problem for the linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit and we discuss its link with the self-shielding effect in nuclear reactor physics. The results presented here have been obtained in collaboration with Harsha Hutridurga and Olga Mula.
• 本セミナーは，日本航空宇宙学会関西支部分科会主催の「運動論方程式，流体力学とその周辺」（第10回）となります．
• 日時：2018年12月28日（金） 15:30-16:30
• 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 111講義室（キャンパスマップ 53番）
• 講師：Prof. Shih-Hsien Yu (Department of Mathematics, National University of Singapore, Singapore)
• 題目：Green's functions and Compressible Navier-Stokes equation
• 要旨：A class of decomposition of Green's functions for the compressible Navier-Stokes
linearized around a constant state is introduced. The singular structures of the Green's functions
are developed as essential devices to use the nonlinearity directly to covert the
2nd order quasi-linear PDE into a system of zero-th order integral equation with regular
integral kernels. The system of integrable equations allows a wider class of functions such as BV solutions.
We have shown global existence and well-posedness of the compressible Navier-Stokes
equation for isentropic gas with the gas constant $\gamma \in (0,e)$ in the Lagrangian
coordinate for the class of the BV functions and point wise $L^\infty$ around a constant state; and the
underline pointwise structure of the solutions is constructed.
• 日時：2018年9月7日（金） 15:00-16:00
• 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 213講義室（キャンパスマップ 53番）
• 講師：Prof. Ansgar Jüngel (Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria)
• 題目：Multicomponent fluids: thermodynamic structure and structure-preserving numerical discretization
• 要旨：Multicomponent fluids can be modeled by parabolic cross-diffusion systems with fluxes which depend on the density gradients of all species. These systems possess a thermodynamic structure that can be translated into a mathematical formulation with nice properties like positivity of the diffusion matrix and boundedness of the mass fractions. For numerical discretizations, it is important to preserve these properties. In this talk, we present structure-preserving finite-volume and finite-element approximations modeling Stefan-Maxwell flows and ion transport through membranes.