New general decay results for a von Karman plate equation with memory-type boundary conditions

Abstract

In this paper we consider a von Karman plate equation with memory-type boundary conditions. By assuming the relaxation function $ k_i $ $ (i = 1, 2) $ with minimal conditions on the $ L^1(0, \infty) $, we establish an optimal explicit and general energy decay result. In particular, the energy result holds for $ H(s) = s^p $ with the full admissible range $ [1, 2) $ instead of $ [1, 3/2) $. This result is new and substantially improves earlier results in the literature.