Almost flat Relaxation Functions in Visco-elasticity

We will consider a problem modeling a viscoelastic material which according to Boltzmann's superposition principle, is obtained from the constitutive relation between the stress and the strain of the material. In this project we would like to weaken further the existing conditions on exponential decay. We intend to enlarge considerably the class of admissible relaxation functions by exploring almost flat functions. This will allow the inclusion of many other viscoelastic materials.

We will consider a problem modeling a viscoelastic material which according to Boltzmann's superposition principle, is obtained from the constitutive relation between the stress and the strain of the material. In this project we would like to weaken further the existing conditions on exponential decay. We intend to enlarge considerably the class of admissible relaxation functions by exploring almost flat functions. This will allow the inclusion of many other viscoelastic materials.