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Optimal decay for plates with rotational inertia and memory
Author(s) -
Oquendo Higidio Portillo,
Astudillo María
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800170
Subject(s) - exponential decay , mathematics , inertia , exponential growth , polynomial , work (physics) , exponential function , moment of inertia , kernel (algebra) , mathematical analysis , exponential stability , classical mechanics , physics , thermodynamics , combinatorics , quantum mechanics , nonlinear system
We study the asymptotic behavior of a linear plate equation with effects of rotational inertia and a fractional damping in the memory term:u t t − γ Δ u t t + β Δ 2 u − ∫ 0 ∞ g ( s ) Δ 2 θ u ( t − s )d s = 0 , where θ ≤ 1 and the kernel g is exponentially decreasing. The main result of this work is the polynomial decay of their solutions when θ < 1 . We prove that the solutions decay with the rate t − 1 / ( 4 − 4 θ )and also that the decay rate is optimal. Furthermore, when θ = 1 , we obtain the exponential decay of the solutions.