Mathematical Sciences: Partial Differential Equations and Applications

9300948 Friedman这个项目涉及偏微分方程中的一些非线性问题。这些问题包括：(a)在研究电照相视觉发展过程中出现的自由边界问题，(b)电照相中电子图像的形成，(c) Navier-Stokes方程的自由边界问题，(d)位错的聚结模型，(e)网络扩散，(f)光漂白的动力学模型，以及(g)动力学条件下的Stefan问题。该研究主要关注由物理模型和工程模型驱动的偏微分方程的非线性问题；其中许多模型直接来自美国工业。这些问题涉及到(1)偏微分方程和系统，它们是非线性的，也可能是退化的，或者（ii）线性偏微分方程和系统在自由边界域中。要考虑的问题来自半导体加工、电子照相和涂层流等领域。＊＊＊

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. ***