Models of Phase Transitions

by Augusto Visintin

Overview

... "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.

Product Details

ISBN-13:	9780817637682
Publisher:	Birkhäuser Boston
Publication date:	12/01/1996
Series:	Progress in Nonlinear Differential Equations and Their Applications , #28
Edition description:	1996
Pages:	326
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Reader’s Guide.- 1. Some Nonlinear P.D.E.s.- Prelude.- I. Models and P.D.E.s.- II. A Class of Quasilinear Parabolic P.D.E.s.- III. Doubly Nonlinear Parabolic P.D.E.s.- 2. Phase Transitions.- IV. The Stefan Problem.- V. Generalizations of the Stefan Problem.- VI. The Gibbs-Thomson Law.- VII. Nucleation and Growth.- VIII. The Stefan-Gibbs-Thomson Problem with Nucleation.- IX. Two-Scale Models of Phase Transitions.- X. Compactness by Strict Convexity.- XI. Toolbox.- Book Selection.

Editorial Reviews

"The book is well organized, concise and clearly written with a strict interplay between physics and mathematics... Largely self-contained ... highly recommended to all graduate students and reserachers in applied mathematics."

—ZAA

From the Publisher