Open AccessExponential decay and global existence of solutions of a singular nonlocal viscoelastic system with distributed delay and damping terms
Author(s) -
Abdelbaki Choucha,
Salah Boulaaras,
Djamel Ouchenane
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2103795c
Subject(s) - mathematics , viscoelasticity , work (physics) , term (time) , exponential decay , exponential stability , mathematical analysis , boundary (topology) , nonlinear system , exponential growth , extension (predicate logic) , exponential function , energy method , energy (signal processing) , control theory (sociology) , physics , computer science , statistics , control (management) , quantum mechanics , artificial intelligence , nuclear physics , thermodynamics , programming language
We investigate in this work a singular one-dimensional viscoelastic system with a nonlinear source term, distributed delay, nonlocal boundary condition, and damping terms. By the theory of potentialwell, the existence of a global solution is established, and by the energy method and the functional of Lyapunov, we prove the exponential decay result. This work is an extension of Boulaaras? work in ([3] and [27]).