Asymptotic behavior to a von Kármán plate with boundary memory conditions

General decay to a von Kármán system with memory

“…In the present work we generalize the earlier decay result to solutions of (1)- (7). More precisely, we show that the energy decays with a similar rate of decay of the relaxation function, which is not necessarily decaying in a polynomial or exponential fashion.…”

“…Note that the exponential and the polynomial decay estimates, given in early works [6] and [7], are only particular cases of (34). More precisely, we obtain exponential decay for ξ (t) = a and polynomial decay for ξ (t) = a(1+t) −1 , where a > 0 is a constant.…”

“…It is shown in these works that these dissipations produce a uniform rate of decay of the solution when t goes to infinity. The problem of stability of the solutions to a von Kármán system for viscoelastic plates with memory and boundary memory conditions was studied by Rivera and Menzala [6] and Rivera et al [7]. They proved that for p > 2 the energy decays uniformly exponentially or algebraically with the same rate of decay as the relaxation function, that is, when the relaxation function decays exponentially, the corresponding solution also decays exponentially.…”

“…In Section 2, we present some notation and material needed for our work and state a global existence theorem, which can be proved following exactly the arguments of [6,7]. In Section 3 we presented some important technical lemmas for obtaining the stability of the system.…”

Exponential decay for a von Kármán equations with memory

“…It is shown in these works that these dissipations produce uniform rate of decay of the solution when t goes to infinity. Rivera and Menzala 16 and Rivera et al 17 studied the stability of the solutions to a von Kármán system for viscoelastic plates with memory and boundary memory conditions. They proved that the energy decays uniformly exponentially or algebraically with the same rate of decay as the relaxation function.…”