Energy Methods for Free Boundary Problems : Applications to Nonlinear PDEs and Fluid Mechanics

An integrated account of modern developments in energy methods for the study of free boundary problems in partial differential equations. The theory presented has relevance to many physical applications, including heat conduction, surface and underground water flow, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, and semiconductors. Part I is an exposition of the methods of several general classes of nonlinear equations and systems. Part II presents applications. Will be useful to applied mathematicians, graduate students, physicists, and engineers.