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Conservation Laws and Transport Problems

  • Hyperbolic Systems of Conservation Laws in One Space Dimension
  • Fundamental theory: existence, uniqueness and continuous dependence of weak entropy admissible solutions, characterization of semigroup trajectories
  • Problems with large BV data, blow-up of BV norm, local existence and uniqueness
  • Structure of solutions, local behavior, structural stability, generalized shift-differentiability w.r.t. parameters
  • Initial-boundary problems, inhomogeneous balance laws, asymptotic blow-up patterns, global existence
  • Convergence rates for approximation schemes: wave-front tracking, Glimm, finite element
  • Vanishing viscosity approximations, a-priori estimates, convergence
Research Group: 
Mathematical Analysis, Modelling, and Applications

Linear wave propagations for half space problems

In this series of talks, we are aimed at constructing the solution formula of the Green's functions for various hyperbolic and hyperbolic-parabolic partial differential equations in a half multi-D space domain. We will use the transform variables to derive a master relationships of the Dirichlet-Neumann data of the PDE, and use it to obtain the full Dirichlet-Neumann data in the transform variables; and obtain the Rayleigh surface.

Conservation Laws and Transport Problems

Research topics

  • Hyperbolic Systems of Conservation Laws in One Space Dimension
  • Fundamental theory: existence, uniqueness and continuous dependence of weak entropy admissible solutions, characterization of semigroup trajectories
  • Problems with large BV data, blow-up of BV norm, local existence and uniqueness
  • Structure of solutions, local behavior, structural stability, generalized shift-differentiability w.r.t. parameters
  • Initial-boundary problems, inhomogeneous balance laws, asymptotic blow-up patterns, global existence
  • Convergence rates for approximation schemes: wave-front tracking, Glimm, finite element
  • Vanishing viscosity approximations, a-priori estimates, convergence
  • Flow of weakly differentiable vector fields
  • Linear transport problems

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