Mathematical Sciences: Partial Differential Equations and Applications

小行星9300948 这个项目是关于偏微分方程中的一些非线性问题。 这些问题包括：（a）在研究电子照相中的视觉发展过程中出现的自由边界问题，（B）电子照相中的电子图像的形成，（c）Navier-Stokes方程的自由边界问题，（d）位错的聚结模型，（e）网络的扩散，（f）光漂白的动力学模型，（g）带动力学条件的Stefan问题。 该研究关注的是物理和工程模型激发的偏微分方程中的非线性问题;其中许多模型直接来自美国工业。 这些问题涉及（1）偏微分方程和系统，这是非线性的，可能退化，以及（ii）线性偏微分方程和系统的区域与自由边界。 要考虑的问题来自半导体加工、电子照相和涂布流程等领域。 ***

9300948 Friedman This project is concerned with a number of nonlinear problems in partial differential equations. These problems include: (a) free boundary problems that arise in studying the visual development in electrophotography, (b) the formation of electric images in electrophotography, (c) free boundary problems for Navier-Stokes equations, (d) coalescence models for dislocations, (e) diffusion of networks, (f) a kinetic model for photobleaching, and (g) the Stefan problem with kinetic condition. The research is concerned with nonlinear problems in partial differential equations as motivated by physical and engineering models; many of these models come directly from U.S. industry. The problems involve either (1) partial differential equations and systems, which are nonlinear and possibly degenerate as well, or (ii) linear partial differential equations and systems in domains with a free boundary. The problems to be considered arise from such areas as semiconductor processing, electrophotography, and coating flows. ***