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

Baowei Feng; Abdelaziz Soufyane

doi:10.3934/dcds.2020092

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2020, Volume 40, Issue 3: 1757-1774. Doi: 10.3934/dcds.2020092

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

Baowei Feng^1, and
Abdelaziz Soufyane^2, ,

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
^* Corresponding author: Abdelaziz Soufyane

Received: May 31, 2019

Revised: September 30, 2019

Published: December 2019

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

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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.

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Mathematics Subject Classification: Primary: 35B40, 93D15; Secondary: 74D99, 93D20.

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