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March  2020, 40(3): 1757-1774. doi: 10.3934/dcds.2020092

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

 1 Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China 2 Department of Mathematics, College of Sciences, University of Sharjah, P.O.Box 27272, Sharjah, UAE

* Corresponding author: Abdelaziz Soufyane

Received  June 2019 Revised  October 2019 Published  December 2019

Fund Project: Baowei Feng has been supported by the National Natural Science Foundation of China grant 11701465. Abdelaziz Soufyane has been supported by University of Sharjah grant 1802144069

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.

Citation: Baowei Feng, Abdelaziz Soufyane. New general decay results for a von Karman plate equation with memory-type boundary conditions. Discrete & Continuous Dynamical Systems - A, 2020, 40 (3) : 1757-1774. doi: 10.3934/dcds.2020092
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