Further Parabolic Evolution Problems

Abstract

In this final chapter, we apply the theory of quasilinear parabolic evolution equations developed in Chapter 5 to several parabolic evolution problems to show the strength of the tools and techniques of this book. These problems include generalized Newtonian flows, nematic liquid crystal flows, Maxwell-Stefan diffusion problems, Stefan problems with variable surface tension, and, last but not least, several classes of geometric evolution equations. By means of our methods, many other parabolic evolution problems can be solved in the same—or at least in a similar—way.