Thermomechanics of Evolving Phase Boundaries in the Plane

This is one of the few books on the subject of mathematical materials science. It discusses the dynamics of two-phase systems within the framework of modern continuum thermodynamics, stressing fundamentals. Two general theories are discussed: a mechanical theory that leads to a generalization of the classical curve-shortening equation and a theory of heat conduction that broadly generalizes the classical Stefan theory. This original survey includes simple solutions that demonstrate the instabilities inherent in two-phase problems. The free-boundary problems that form the basis of the subject should be of great interest to mathematicians and physical scientists.

This is one of the few books on the subject of mathematical materials science. It discusses the dynamics of two-phase systems within the framework of modern continuum thermodynamics, stressing fundamentals. Two general theories are discussed: a mechanical theory that leads to a generalization of the classical curve-shortening equation and a theory of heat conduction that broadly generalizes the classical Stefan theory. This original survey includes simple solutions that demonstrate the instabilities inherent in two-phase problems. The free-boundary problems that form the basis of the subject should be of great interest to mathematicians and physical scientists.

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The author emphasizes issues that are foundational in nature, being more interested in the interplay between mathematics and physics than the solution of specific problems. The mathematical issues of existence, uniqueness, and regularity of solutions are discussed only superficially. Topics include curves, phase regions, control volumes, inflows, balance of forces, constitutive theory, unstable interfacial energies and interfaces with corners, thermodynamics of two-phase systems, and free-boundary problems. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Carnegie Mellon University