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Exponential decay for a nonlinear axially moving viscoelastic string
Author(s) -
Kelleche Abdelkarim,
Tatar Nassereddine
Publication year - 2020
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.6932
Subject(s) - axial symmetry , viscoelasticity , string (physics) , mathematics , nonlinear system , relaxation (psychology) , term (time) , exponential decay , mathematical analysis , exponential function , control theory (sociology) , boundary value problem , exponential stability , exponential growth , controller (irrigation) , physics , geometry , computer science , control (management) , mathematical physics , quantum mechanics , nuclear physics , thermodynamics , psychology , social psychology , artificial intelligence , biology , agronomy
This paper is concerned with the stabilization of a nonlinear axially moving viscoelastic string. First, we show under suitable conditions on the initial data that solutions exist globally by using the potential well method. Then, we prove that the produced damping by the viscoelastic term is sufficient to guarantee an exponential decay of solutions. This is established by imposing weaker conditions than the commonly used ones on the relaxation function and by utilizing an appropriate boundary controller.