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Uniform decay rate estimates for the beam equation with locally distributed nonlinear damping
Author(s) -
Cavalcanti Marcelo M.,
Delatorre Leonel G.,
Domingos Cavalcanti Valéria N.,
Gonzalez Martinez Victor H.,
Soares Daiane C.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7407
Subject(s) - mathematics , observability , bounded function , mathematical analysis , nonlinear system , domain (mathematical analysis) , limit (mathematics) , continuation , uniform boundedness , beam (structure) , phase space , space (punctuation) , physics , linguistics , philosophy , quantum mechanics , computer science , optics , thermodynamics , programming language
In this paper, we study the semilinear beam equation with a locally distributed nonlinear damping on a smooth bounded domain. We first construct approximate solutions, and we show that the aforementioned approximate solutions decay uniformly in the weak phase space by using an observability inequality associated to the linear problem and a unique continuation property. Then, we prove the global existence as well as the uniform decay of solutions for the original model by passing to the limit and using a weak lower semicontinuity argument, respectively.