Exponential decay and global existence of solutions of a singular nonlocal viscoelastic system with distributed delay and damping terms | Zendy

Abdelbaki Choucha | Zendy; Salah Boulaaras | Zendy; Djamel Ouchenane | Zendy

Open Access

Exponential 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]).

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