9802426 Daskalopoulos This Americas Program award will fund a collaborative study in certain non-linear parabolic equations in differential geometry between Dr. Panagiota Daskalopolous, University of California, Irvine, and Dr. Manuel del Pino, University of Chile. The main objectives of the proposal are concerned with the study of the structure and the new features of certain nonlinear degenerate parabolic equations arising in different geometry and physical applications. The study will include investigation of several aspects of the subject, including super-diffusive nonlinear parabolic problems, the vanishing profile of fast-diffusions, and the free-boundary for the porous medium equation with prescribed boundary conditions. The researchers' main interest is in understanding the similarities and differences between the case of slow diffusion, and the cases of fast diffusion because of their connection to differential geometry and their occurrence in a number of physical applications, including thin liquid film dynamics and the expansion of a thermalized electron cloud. ***
