## Free Boundary Problems Involving SolidsThis is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined. |

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### Contents

Blanchard and P Nicolas | 7 |

P Colli and A Visintin | 14 |

Frémond | 20 |

Greenberg | 28 |

A Klarbring A Mikelic and M Shillor | 35 |

T | 41 |

Reddy | 48 |

### Common terms and phrases

Anal analysis anisotropy applications approximation assume asymptotic boundary conditions bounded Caginalp Chadam classical Stefan coefficients Collège de France computed consider constant contact problem convergence convex convex set defined denotes density derivative diffusion discrete interface domain drum dynamics elastic elastoplasticity enthalpy estimates evolution existence finite element flattened formulation Free boundary problems free energy friction function given global heat Lemma linear Lipschitz Lipschitz continuous lower semicontinuous Math Mathematics matrix mean curvature mesh method monotone mushy region Nochetto normal numerical obtained operator PAolini parabolic equations partial differential equations phase field equations phase field model phase transitions physical plastic proof regularity satisfies sharp interface Shillor solid solidification space stability Stefan problem subdifferential surface tension temperature Theorem theory thermoelasticity two-phase Stefan problem Tyield unique solution value problem variables variational inequality velocity Volume weak solution zero