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Global existence and decay of solutions of a singular nonlocal viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized damping term
Journal article   Peer reviewed

Global existence and decay of solutions of a singular nonlocal viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized damping term

Salah Boulaaras and Nadia Mezouar
Mathematical methods in the applied sciences, Vol.43(10), pp.6140-6164
15/07/2020
DOI: https://doi.org/10.1002/mma.6361

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
The paper deals with the existence of a global solution of a singular one-dimensional viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized frictional damping a(x)u(t) using the potential well theory. Furthermore, the general decay result is proved. We construct a suitable Lyapunov functional and make use of the perturbed energy method.

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