Mathematical Sciences: Partial Differential Equations and Applications

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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. ***