We show how the so-called von Kármán model can be obtained as a singular limit
of a Mindlin–Timoshenko system when the modulus of elasticity in shear
tends to infinity. This result gives a positive answer to a conjecture by
Lagnese and Lions in 1988. Introducing damping mechanisms, we also
show that the energy of solutions for this modified Mindlin–Timoshenko
system decays exponentially, uniformly with respect to the parameter
. As
, we
obtain the damped von Kármán model with associated energy exponentially
decaying to zero as well.
Dedicated to Enrique Fernández-Cara on
the occasion of his 60th birthday
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