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We determine completely the exact Riemann solutions for the system of Euler equations in a duct with discontinuous varying cross–section. The crucial point in solving the Riemann problem for hyperbolic system is the construction of the wave curves. To address the difficulty in the construction due to the nonstrict hyperbolicity of the underlying system, we(More)
The morphology of micrometre-size particulate matter is of critical importance in fields ranging from toxicology to climate science, yet these properties are surprisingly difficult to measure in the particles' native environment. Electron microscopy requires collection of particles on a substrate; visible light scattering provides insufficient resolution;(More)
The classical two-phase flow model of Baer and Nunziato is generalized to a thermody-namic consistent multi-component model in multi dimensions. The extended model allows to deal with phase transitions where exchange processes are modeled by relaxation terms. In particular, chemical relaxation is based on chemical potentials instead of Gibbs free energies.(More)
A class of non-equilibrium models for compressible multi-component fluids in multi-dimensions is investigated taking into account viscosity and heat conduction. These models are subject to the choice of interfacial pressures and interfacial velocity as well as relaxation terms for velocity, pressure, temperature and chemical potentials. Sufficient(More)
The paper deals with the Robin function and eigenvalue problems generated by the Robin operator. First we show that Green's function of an n-fold connected domain is the Robin function of an appropriate simply connected domain. The main part of the paper deals with eigenvalue problems for the Robin operator: the mixed Stekloff eigenvalue problem and the(More)
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