In this paper, we consider a nonlinear Timoshenko system, in a bounded domain, where the memory-type damping is acting on a part of the boundary. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. Our work allows certain relaxation functions which are not necessarily of exponential or polynomial decay and, therefore, generalizes and improves earlier results in the literature.
"General decay of solutions of a nonlinear Timoshenko system with a boundary control of memory type." Differential Integral Equations 22 (11/12) 1125 - 1139, November/December 2009. https://doi.org/10.57262/die/1356019408