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J. M. Ball, “Initial-Boundary Value Problems for an Extensible Beam,” Journal of Mathematical Analysis and Applications, Vol. 42, No. 1, 1973, pp. 61-90. doi:10.1016/0022-247X(73)90121-2

has been cited by the following article:

• TITLE: Boundary Stabilization of a More General Kirchhoff-Type Beam Equation

  AUTHORS: Jianwen Zhang, Danxia Wang

  KEYWORDS: Kirchhoff-Type Beam; Non-Linear Boundary; Global Solutions; Exponential Decay

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.1 No.3, September 28, 2012

  ABSTRACT: Simultaneously, considering the viscous effect of material, damping of medium, geometrical nonlinearity, physical nonlinearity, we set up a more general equation of beam subjected to axial force and external load. We prove the existence and uniqueness of global solutions under non-linear boundary conditions which the model is added one damping mechanism at l end. What is more, we also prove the exponential decay property of the energy of above mentioned system.