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 memorytype boundary conditions. By assuming the relaxation function k i (i = 1, 2) with minimal conditions on the L 1 (0, ∞), 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.

Optimal decay rates of a nonlinear suspension bridge with memories

“…We point out here that our argument is close to the one in Feng and Soufyane, 23 with the necessary modifications required by the nature of our model.…”

Arbitrary decay for a von Karman system with memory

“…For the case k = h = 0 in (1.1) with memory-type boundary condition, Feng and Soufyane [14] obtained an optimal explicit and general energy decay result. For more results on von Karman plate equation with memory-type boundary condition, we refer to [15,16].…”

Memory‐type boundary stabilization of a transmission problem for Kirchhoff wave equations

“…Wu 11 used this assumption to study a Kirchhoff-type wave equation. Please see previous studies, [12][13][14][15][16][17][18][19] etc., for the results on wave equations with boundary condition of memory type.…”