Arabian Journal of Mathematics (Dec 2022)

Global existence and asymptotic behavior for a Timoshenko system with internal damping and logarithmic source terms

  • Sebastião Martins Siqueira Cordeiro,
  • Ducival Carvalho Pereira,
  • Carlos Alessandro da Costa Baldez,
  • Carlos Alberto Raposo da Cunha

DOI
https://doi.org/10.1007/s40065-022-00411-y
Journal volume & issue
Vol. 12, no. 1
pp. 105 – 118

Abstract

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Abstract This manuscript deals with a Timoshenko system with damping and source. The existence and stability of the solution are analyzed taking into account the competition of the internal damping versus the logarithmic source. We use the potential well theory. For initial data in the stability set created by the Nehari surface, the existence of global solutions is proved using Faedo–Galerkin’s approximation. The exponential decay is given by the Nakao theorem. A numerical approach is presented to illustrate the results obtained.

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