9322146 Strauss Stability and instability phenomena will be investigated in the kinetic theory of charged particles both with and without collisions. Also to be studied are harmonic maps in Minkowski space, and the stability theory of time- dependent ground states of scalar fields, including the effects of boundaries. A further focus of research is the smoothing phenomenon for linear and nonlinear dispersive waves.Advanced semiconductor devices, used for computer chips, are made of materials whose properties derive from the movements of negative electrons and positive "holes". Such movements form a type of nonlinear wave and are described by certain mathematical equations. We study how these movements change and how they are sensitive to initial variations. The same kinds of equations describe many other wave phenomena in science and engineering, such as in energy research and space research. The sensitivity of nonlinear waves is studied in a variety of contexts. The purpose is to determine the fundamental reasons for the unstable behavior of waves.Walter Strauss
