- 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:

## 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