A Nonlinear Hyperbolic Volterra Equation in Viscoelasticity [report]

C. M. Dafermos, J. A. Nohel
1980 unpublished
A general model for the nonlinear motion of a one dimensional, finite, homogeneous, viscoelastic body is developed and analysed by an energy method. It is shown that under physically reasonable conditions the nonlinear boundary, initial value problem has a unique, smooth solution (global in time), provided the given data are sufficiently "small" and smooth; moreover, the solution and its derivatives of first and second order decay to zero as t + -. Various modifications and generalizations,
more » ... eneralizations, including two and three dimensional problems, are also discussed.
doi:10.21236/ada089668 fatcat:d25h4o4dvrafzmhffdopfijxbi