9403399 Conlon The principal investigator will conduct research on problems in partial differential equations. These problems are motivated by intuitions concerning the behavior of interacting random walks over large time scales. A major step in this direction would be to understand random walks in random environments. The principal investigator's approach to these problems has been to obtain sufficiently sharp estimates on solutions to appropriate partial differential equations. He intends to continue this work. The general goal of this project is to advance understanding of diffusion in a medium where the consistency of the medium changes a lot. When two liquids are mixed the process of mixing is a diffusive process. Heat propagates largely by diffusion. There are many examples of diffusive processes where the consistency of the medium of propagation changes a lot.One example is the propagation of oil through porous rock. Another is the propagation of pollutants in the ground. In each of the above examples it is important to build up a qualitative understanding of the mechanism of difdusion in such media. This study will contribute to this,
