U.S.-Chile Cooperative Research: Nonlinear Degenerate Parabolic Problems

9802426 Daskalopoulos美洲项目奖将资助加州大学欧文分校Panagiota Daskalopolous博士和智利大学Manuel del Pino博士在微分几何中某些非线性抛物方程的合作研究。本文的主要目的是研究在不同几何和物理应用中出现的某些非线性退化抛物方程的结构和新特征。本研究将包括研究该主题的几个方面，包括超扩散非线性抛物问题，快速扩散的消失剖面，以及具有规定边界条件的多孔介质方程的自由边界。研究人员的主要兴趣在于理解慢扩散和快速扩散之间的异同，因为它们与微分几何的联系以及它们在许多物理应用中的出现，包括薄液膜动力学和热化电子云的膨胀。* * *

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. ***