Numerical Aspects of Hyperbolic Balance Laws and Related Problems

A wide range of phenomena in science and technology may be described by nonlinear partial differential equations, characterizing systems of conservation laws with source terms.

Well known examples are hyperbolic systems with source terms, kinetic equations and convection-reaction-diffusion equations. This class of equations fits several fundamental physical laws and plays a crucial role in applications ranging from plasma physics and geophysics to semiconductor design and granular gases.Recent studies employ the aforementioned theoretical background in order to describe the collective motion of a large number of particles such as: pedestrian and traffic flows, swarming dynamics, opinion control, diffusion of tumor cells and the cardiovascular system.

Goal of the present Workshop is to present some recent numerical results for these problems with a particular focus on multiple scales.