The stability number of the Timoshenko system with second sound
ML Santos, DSA Júnior, JEM Rivera - Journal of Differential Equations, 2012 - Elsevier
In this work, we consider the Timoshenko beam model with second sound. We introduce a
new number χ0 that characterizes the exponential decay. We prove that the corresponding
semigroup associated to the system is exponentially stable if and only if χ0= 0. Otherwise
there is a lack of exponential stability. In this case we prove that the semigroup decays as t−
1/2. Moreover we show that the rate is optimal.
new number χ0 that characterizes the exponential decay. We prove that the corresponding
semigroup associated to the system is exponentially stable if and only if χ0= 0. Otherwise
there is a lack of exponential stability. In this case we prove that the semigroup decays as t−
1/2. Moreover we show that the rate is optimal.
[PDF][PDF] The stability number of the Timoshenko system with second sound J
ML Santosa, DSA Júniora, JEM Rivera - Diff. Eq, 2012 - academia.edu
Here we will consider a fully hyperbolic thermoelastic beam model. That is to say, instead of
the classical thermoelastic system defined by the Euler–Bernoulli equation coupled with the
(parabolic) heat equations, we will use the Timoshenko system coupled to a hyperbolic heat
model defined by the Cattaneo law. From our point of view this model explains better the
thermoelastic phenomenon.
the classical thermoelastic system defined by the Euler–Bernoulli equation coupled with the
(parabolic) heat equations, we will use the Timoshenko system coupled to a hyperbolic heat
model defined by the Cattaneo law. From our point of view this model explains better the
thermoelastic phenomenon.
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