Nonlinear diffusion equations and their equilibrium states, 3 Book

Nonlinear diffusion equations have long played a crucial role in the theory of partial differential equations. They have posed challenging and deep mathematical questions and found important applications in many areas of science and technology. Examples of particular interest are biological and chemical pattern formulation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. All of these topics, and more, are treated in this volume of refereed and revised papers. The study of special solutions leads to problems in ordinary differential equations going back to the beginning of the century, as in the classical Emden-Fowler theory, motivated by questions in astrophysics. Recently, with many new questions and equations, this theory has returned to the center of developments. The papers in this volume represent a broad spectrum of work at the cutting edge of these theories. This volume had its origins in the highly acclaimed Gregynog, Wales, August 1989 session of an ongoing series that began at the Mathematical Sciences Research Center. In this area of endeavor, this series of conferences serves as an important vehicle to disseminate information and highlight new developments. Research workers in applied mathematics, engineering, physics, chemistry, and biology will be interested both for themselves and for their graduate students.