Global Existence of Classical Solutions to the Equations of Motion for Materials with Fading Memory

In this paper, the authors discuss global existence of classical solutions to the equations of motion for a class of nonlinear materials obeying Coleman and Noll's principle of fading memory. In order to highlight the main ideas about the effects of memory and avoid significant technical complications, the people consider only one-dimensional motions. They discuss the relevant mechanical aspects of materials with fading memory and formulate an appropriate class of dynamic problems. For materials with memory, the stress at the present time can be affected by the entire temporal history of the motion. A simple example of a material with fading memory is provided by linear viscoelasticity of the Boltzmann type. The authors discuss global existence of solutions to the history value problem.