Determining solutions of hyperbolic systems from incomplete data

An investigation is conducted regarding first-order hyperbolic systems of partial differential equations, taking into account problems for which complete initial data are not available. Problems of the considered kind arise in geophysical applications where satellites are used to collect data. In global weather prediction, it is possible to derive atmospheric temperature and pressure reasonably well over the whole globe from satellite measurements; obtaining the wind field globally is more difficult. It is pointed out that a simple model of atmospheric flow investigated in numerical weather prediction is governed by the shallow water equations. The effect of the Coriolis term on the linearized shallow-water equations is studied.