• 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.