Signorini's problem for the Bresse beam model with localized Kelvin-Voigt dissipation

We prove the existence of a global solution to Signorini's problem for the localized viscoelastic Bresse beam model (circular arc) with continuous and discontinuous constitutive laws. We show that when the constitutive law is continuous, the solution decays exponentially to zero, and when the constitutive law is discontinuous the solution decays only polynomially to zero. The method we use for proving our result is different the others already used in Signorini's problem and is based on approximations through a hybrid model. Also, we present some numerical results using discrete approximations in time and space, based on the finite element method on the spatial variable and the implicit Newmark method to the discretized the temporal variable. For more information see https://ejde.math.txstate.edu/Volumes/2024/17/abstr.html