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Pile-Up Solutions for a Mixed System of Conservation Laws Modelling Dislocation Interaction in Crystals

In: Applied and Industrial Mathematics, Venice—2, 1998

Author

Listed:
  • A. Carpio

    (Universidad Complutense de Madrid, Departamento de Matemática Aplicada)

  • J. J. L. Velazquez

    (Universidad Complutense de Madrid, Departamento de Matemática Aplicada)

  • S. J. Chapman

    (University of Oxford, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute)

Abstract

A continuum model for dislocation interaction in a simple crystal geometry is proposed. Our model accounts for the formation of structures such as dislocation pile-ups. Pattern formation is this model is related to the loss of strict hyperbolicity in the system and the appearance of instabilities.

Suggested Citation

  • A. Carpio & J. J. L. Velazquez & S. J. Chapman, 2000. "Pile-Up Solutions for a Mixed System of Conservation Laws Modelling Dislocation Interaction in Crystals," Springer Books, in: Renato Spigler (ed.), Applied and Industrial Mathematics, Venice—2, 1998, pages 219-228, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-4193-2_14
    DOI: 10.1007/978-94-011-4193-2_14
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