Decay and numerical results in nonsimple viscoelasticity

In this paper, we give some mathematical and numerical results on the behavior of a nonsimple viscoelastic plate corresponding to anti-plane shear deformations. First, we derive briefly the equations of the considered plate, and then, we study the well-posedness problem. Second, we prove that the solutions decay exponentially at a rate proportional to the total mass of the second order. Finally, we give some numerical experiments based on the spectral method developed for multi-dimensional problems with implementation in MATLAB for one and two-dimensional spaces.