Models of Phase Transitions

Description

.. "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/: " "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple .... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in- tended 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. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX Front Matter....Pages i-ix Introduction....Pages 1-5 Models and P.D.E.s....Pages 6-30 A Class of Quasilinear Parabolic P.D.E.s....Pages 31-67 Doubly Nonlinear Parabolic P.D.E.s....Pages 68-89 The Stefan Problem....Pages 90-122 Generalizations of the Stefan Problem....Pages 123-154 The Gibbs-Thomson Law....Pages 155-177 Nucleation and Growth....Pages 178-202 The Stefan-Gibbs-Thomson Problem with Nucleation....Pages 203-228 Two-Scale Models of Phase Transitions....Pages 229-247 Compactness by Strict Convexity....Pages 248-259 Toolbox....Pages 260-294 Back Matter....Pages 295-325