The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation.
Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions...
We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.