Visintin A. Models of Phase Transitions

Birkhauser Boston, Springer, 1996. — 334 p. — (Progress in Nonlinear Differential Equations and Their Applications 28). — ISBN-13 978-1-4612-8641.This volume illustrates some aspects of the mathematical treatment of phase
transitions, namely, the classical Stefan problem and its generalizations. The intended reader is a researcher in application-oriented mathematics. An effort has
been made to make a part of the book accessible to beginners, as well as physicists
and engineers with a mathematical background. Some room has also been devoted
to illustrate analytical tools.Models and P.D.E.s
A Class of Quasilinear Parabolic P.D.E.s
Doubly Nonlinear Parabolic P.D.E.s
The Stefan Problem
Generalizations of the Stefan Problem
The Gibbs-Thomson Law
Nucleation and Growth
The Stefan-Gibbs-Thomson Problem with Nucleation
Two-Scale Models of Phase Transitions
Compactness by Strict Convexity
Toolbox