Abstract
We study the asymptotic behavior of solutions to an equation describing non-linear vibration of a string with viscosity. In the case when the string is unstretched (the degenerate case), we determine the decay order of solutions by investigating the dynamics near an infinite-dimensional center manifold. Moreover, we classify the asymptotic behavior of all solutions from a dynamical systems point of view. We also deal with the case where the string is stretched (the nondegenerate case).
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Mizumachi, T. The asymptotic behavior of solutions to the Kirchhoff equation with a viscous damping term. J Dyn Diff Equat 9, 211–247 (1997). https://doi.org/10.1007/BF02219221
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DOI: https://doi.org/10.1007/BF02219221