Abstract
In this paper we consider a von Karman plate system with memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. We establish an explicit and general decay rate result using some properties of the convex functions. Our result is obtained without imposing any restrictive assumptions on the behavior of the relaxation function at infinity. These general decay estimates extend and improve on some earlier results-exponential or polynomial decay rates.
Highlights
1 Introduction This paper is concerned with the general decay of the solutions to a von Kármán plate system with memory condition at the boundary: utt + u = [u, v] in × (, ∞), ( . )
We prove the general decay of the solution for a von Kármán plate system with memory boundary conditions ( . )-( . ) for resolvent kernels ki satisfying ki (t) ≥ H –ki(t), ∀t ≥ (i =, ), ( . )
In Section we prove the general decay of the solutions to the von Kármán plate system with memory condition at the boundary
Summary
1 Introduction This paper is concerned with the general decay of the solutions to a von Kármán plate system with memory condition at the boundary: utt + u = [u, v] in × ( , ∞), Raposo and Santos [ ] proved the general decay of the solutions to von Kármán plate model Kang [ ] established an explicit and general decay rate result for von Kármán system
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