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The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity

  • Helmut Abels
  • Maria Giovanna MoraEmail author
  • Stefan Müller
Article

Abstract

The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness h of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of h, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von Kármán plate equation.

Mathematics Subject Classification (2000)

74K20 74B20 74H10 35L70 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Helmut Abels
    • 1
  • Maria Giovanna Mora
    • 2
    Email author
  • Stefan Müller
    • 3
  1. 1.NWF I—MathematikUniversität RegensburgRegensburgGermany
  2. 2.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  3. 3.Hausdorff Center for MathematicsUniversität BonnBonnGermany

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