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Weak Solutions to a Model for Crystal Growth from the Melt in Changing Magnetic Fields

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Optimal Control of Coupled Systems of Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 158))

Abstract

We present a model for crystal growth from the melt that accounts for the interaction between melt flow, heating process, and additional applied alternating or travelling magnetic fields. Functional setting and variational formulation are derived for the quasi-stationary approximation of the model.

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Author information

Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117, Berlin, Germany

    Pierre-Étienne Druet

Authors
  1. Pierre-Étienne Druet
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Editor information

Editors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Karl Kunisch

  2. Abt. Partielle Differentialgleichung Weierstraß-Institut für Angewandte Analysis und Stochastik, Humboldt-Universität zu Berlin, Mohrenstrasse 39, 10117, Berlin, Germany

    Jürgen Sprekels

  3. LS Angewandte Mathematik II Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstrasse 3, 91058, Erlangen, Germany

    Günter Leugering

  4. Institut für Mathematik Fak. II Mathematik & Naturwissenschaften, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Fredi Tröltzsch

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Druet, PÉ. (2009). Weak Solutions to a Model for Crystal Growth from the Melt in Changing Magnetic Fields. In: Kunisch, K., Sprekels, J., Leugering, G., Tröltzsch, F. (eds) Optimal Control of Coupled Systems of Partial Differential Equations. International Series of Numerical Mathematics, vol 158. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8923-9_7

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