Free Boundary Value Problems

1. Front Matter

   Pages I-VII

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2. Dynamics of Non-Isothermal Phase Separation

   • Hans Wilhelm Alt, Irena Pawlow

   Pages 1-26

3. Temperature Dependence of Hysteresis in Pseudoelasticity

   • Michel Bornert, Ingo Müller

   Pages 27-35

4. The Numerical Solution of a Continuous Casting Problem

   • J. N. Dewynne, S. D. Howison, John R. Ockendon

   Pages 36-45

5. Global Existence and Stability of Solutions to the Phase Field Equations

   • C. M. Elliott, Zheng Songmu

   Pages 46-58

6. Damping of Shallow Water Waves

   • Ronald B. Guenther, John A. Crow

   Pages 59-65

7. On One Identification Problem in Linear Elasticity

   • J. Haslinger, P. Neittaanmäki

   Pages 66-84

8. Regularity, Uniqueness and Numerical Experiments for a Relaxed Optimal Design Problem

   • Bernhard Kawohl

   Pages 85-100

9. A New Proof of the Uniqueness of Solutions to Two-Phase Stefan Problems for Nonlinear Parabolic Equations

   • Nobuyuki Kenmochi

   Pages 101-126

10. Periodic Stability of Flow in Partially Saturated Porous Media

    • Nobuyuki Kenmochi, Masahiro Kubo

    Pages 127-152

11. Numerical Solution of Diffusion Problems with Non-Local Free Boundary Conditions

    • Gunter H. Meyer

    Pages 153-164

12. Computing Stability Bounds for Thermocapillary Convection in a Crystal-Growth Free Boundary Problem

    • Hans D. Mittelmann

    Pages 165-180

13. Selfadaptive Mesh Modification for Parabolic FBPs: Theory and Computation

    • R. H. Nochetto, M. Paolini, C. Verdi

    Pages 181-206

14. Optimal Control of Systems Governed by Hemivariational Inequalities. Necessary Conditions

    • P. D. Panagiotopoulos

    Pages 207-228

15. On a Steady-State Two-Phase Stefan Problem with Extraction

    • José Francisco Rodrigues

    Pages 229-240

16. Numerical Solution of Hydrodynamic Free Boundary Problems

    • Joel C. W. Rogers, William G. Szymczak, Alan E. Berger, Jay M. Solomon

    Pages 241-266

17. A Finite-Element Approximation of Stefan Problems in Heterogeneous Media

    • Tomáš Roubíček

    Pages 267-275

This monograph contains a collection of 16 papers that were presented at the confer­ ence "Free Boundary Problems: Numerical 7reatment and Optimal Control", held at the Mathematisches Forschungsinstitut Oberwolfach, West Germany, July 9-15, 1989. It was the aim of the organizers of the meeting to bring together experts from different areas in the broad field of free boundary problems, where a certain emphasis was given to the numerical treatment and optimal control of free boundary problems. However, during the conference also a number papers leading to important new theoretical insights were presented. The strong connection between theory and applications finds its reflection in this monograph which contains papers of high theoretical and numerical interest, as well as applications to important practical problems. Many of the contributions are concerned with phase transition phenomena, a field which was of particular importance during the meeting; topics like spinodal decomposition, shape memory alloys, crystal growth and flow through porous media are addressed. Another field of major interest during the con­ ference was fluid flow; also this field is addressed in this volume. The volume opens with a contribution by H. W. Alt and I. Pawlow. In their paper the problem of spinodal decomposition is treated in the non-isothermal situation. For the first time the existence of a weak solution to the corresponding system of evolution equations could be proved. The results of some numerical experiments are also reported. In the following paper, M. Bornert and I.

• Boundary value problem
• elasticity
• evolution
• growth

• Institut für Mathematik, Universität Augsburg, Augsburg, Germany

  K.-H. Hoffmann

• Fachbereich 10 — Bauwesen, Universität-GH Essen, Essen, Germany

  J. Sprekels

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