@article{Kang2024, 
author = {Jum-Ran Kang},
title = {General decay of solutions for a von Karman plate system with general type of relaxation functions on the boundary},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {2308-2325},
keywords = {von Karman plate, general decay, memory term, relaxation function, convexity, boundary condition},
url = {https://www.sciopen.com/article/10.3934/math.2024114},
doi = {10.3934/math.2024114},
abstract = {In this paper, we investigate a von Karman plate system with general type of relaxation functions on the boundary. We derive the general decay rate result without requiring the assumption that the initial value        w    0    ≡  0 on the boundary, using the multiplier method and some properties of the convex functions. Here we consider the resolvent kernels        k    i    (  i  =  1  ,  2  ), namely        k    i    ″    (  t  )  ≥  −      ξ    i    (  t  )      G    i    (  −      k    i    ′    (  t  )  ), where        G    i   are convex and increasing functions near the origin and        ξ    i   are positive nonincreasing functions. Moreover, the energy decay rates depend on the functions        ξ    i   and        G    i    . These general decay estimates allow for certain relaxation functions which are not necessarily of exponential or polynomial decay and therefore improve earlier results in the literature.}
}