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On the Existence of Symmetric Three Dimensional Finger Solutions

In: Recent Progress in Computational and Applied PDES

Author

Listed:
  • Jianzhong Su

    (The University of Texas at Arlington, Department of Mathematics)

  • Bao Loc Tran

    (The University of Texas at Arlington, Department of Mathematics)

Abstract

In this note, the existence problem of symmetric 3-dimenensional finger solutions of Mullins-Sekerka equation is studied. The finger solutions are traveling wave solutions whose finger-shaped interfaces are moving along a certain direction at a constant speed within a cylindrical domain. The existence of finger solutions is shown through a fixed point argument of the Hilbert Transformation.

Suggested Citation

  • Jianzhong Su & Bao Loc Tran, 2002. "On the Existence of Symmetric Three Dimensional Finger Solutions," Springer Books, in: Tony F. Chan & Yunqing Huang & Tao Tang & Jinchao Xu & Long-An Ying (ed.), Recent Progress in Computational and Applied PDES, pages 309-321, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-0113-8_22
    DOI: 10.1007/978-1-4615-0113-8_22
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