Stability in Thermoviscoelasticity with Second Sound

摘要

Here we consider a string composed by three different materials: thermo elastic, viscoelastic and elastic. Our main result is that the exponential stability depends on the position of each material. That is, we prove that the model is exponentially stable if and only if the viscoelastic material is not in the center of the string. Otherwise, there is not exponential stability and the corresponding semigroup also goes to zero, but now polynomially.