## Free Boundary Problems, Theory and ApplicationsAddressing various aspects of nonlinear partial differential equations, this volume contains papers and lectures presented at the Congress on Free boundary Problems, Theory and Application held in Zakopane, Poland in 1995. Topics include existence, uniqueness, asymptotic behavior, and regularity of solutions and interfaces. |

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### Contents

P Colli G Savare Time discretization of Stefan problems with singular heat flux | 16 |

Rubinstein B Zaltzman Morphological instability of the similarity solutions | 29 |

A Tarzia C Turner The onephase supercooled Stefan problem | 43 |

FBPs in phase transitions phase separation and related topics | 59 |

J W Cahn A NovickCohen Limiting motion for an AllenCahnCahnMilliard | 89 |

N Kenmochi Global attractor of the semigroup associated to a phasefield model | 111 |

T Koyama On a heat equation with hysteresis in the source term | 126 |

N Sato Periodic solutions of phase field equations with constraint | 145 |

T Roubicek Modelling of micro structure governed by nonquasiconvex variational | 264 |

A Stancu Selfsimilarity in the deformation of planar convex curves | 271 |

Vazquez The free boundary problem for the heat equation with fixed gradient | 277 |

A Glitzky R Hiinlich Electroreactiondiffusion systems for heterostructures | 305 |

Homberg An extended model for phase transitions in steel | 314 |

B Nedjar Damage gradient of damage and free boundaries | 333 |

J Steinbach Simulation of the mould filling process by means of a temperature | 344 |

Andreucci A Fasano R Gianni M Primicerio R Ricci Diffusion driven | 359 |

P Strzelecki Quasilinear elliptic systems of GinzburgLandau type | 158 |

Blanchard Renormalized solutions for parabolic problems with L1 data | 177 |

H Giga Y Giga Consistency in evolutions by crystalline curvature | 186 |

R Goglione M Paolini Numerical simulations of crystalline motion by mean cur | 203 |

J Kacur Solution of degenerate parabolic problems by relaxation schemes | 217 |

Korten Uniqueness for the Cauchy problem with measures as data | 231 |

A Lapin Weak solutions for nonlinear fluid flow through porous medium | 242 |

J F Rodrigues L Santos On the glacier kinematics with the shallowice approxi | 254 |

A Bonami D Hilhorst E Logak M Mimura A free boundary problem arising | 368 |

K Kuczera Free energy simulations in chemistry and biology | 374 |

B Lesyng Structure and dynamics of biomolecular systems Basic problems | 392 |

J Maskawa T Takeuchi Phase separation in elastic bodies pattern formation | 400 |

Rozyczka T Plewa A Kudlicki Structure formation in cosmology | 408 |

E Wimmer Challenges for computational materials design | 423 |

Wrzosek On an infinite system of reactiondiffusion equations in the theory | 441 |

### Common terms and phrases

Anal analysis anisotropic Appl applied approach approximation assume assumptions asymptotic atoms blow-up point boundary conditions calculations classical coefficient computational consider continuous function convergence convex convex function corresponding crystal crystalline curve damage defined denote density derived diffusion dxds electronic elliptic estimate evolution existence finite flow formulation free boundary problem geometry given global gradient heat equation Hence hysteresis initial data integral interactions interface Kenmochi Lemma limit limsup linear Lipschitz continuous materials Math mathematical maximum principle mean curvature method minimizing molecular dynamics monotone Moreover motion nonlinear obtain parabolic equations parameter perturbations phase field phase transitions Phys physical polygonal polymers positive constant potential properties prove quantum quantum mechanical respectively satisfies self-similar self-similar solutions simulations smooth space Stefan problem structure surface temperature term theory unique solution variational inequality velocity weak solution weakly Wulff shape zero

### Popular passages

Page 300 - Caffarelli and L. Nirenberg, Uniform estimates for regularization of free boundary problems, In: "Analysis and Partial Differential Equations", Marcel Dekker, New York, 1990. [BrL] H. Berestycki, B. Larrouturou, "Mathematical modelling of planar flame propagation" Pitman Research Notes in Mathematics, Longman, London, 1990.