The principal investigator will continue his research on several topics in the dynamics of continua. In particular, he will study continuum and kinetic theories of material motion undergoing phase transitions, initial value problems for the Riemann problem for systems of hyperbolic conservation laws, and distributed-parameter control systems. The tools used will be various techniques from the qualitative theory of partial differential equations and from nonlinear analysis. Many natural phenomena involve the transition of a material from one phase to another. As an example, think of what happens to the ice cubes in your drink. The principal investigator will apply modern methods of nonlinear analysis to study the dynamical behavior of materials undergoing phase transitions and also ways to control the instabilities that often result when materials are stressed.
