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Global existence and decay of solutions of a singular nonlocal viscoelastic system. (English) Zbl 1437.35464

Summary: In this work, we consider a singular one-dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition. By using the potential well theory we obtain the existence of a global solution. Then, we prove the general decay result, by constructing Lyapunov functional and using the perturbed energy method.

MSC:

35L53 Initial-boundary value problems for second-order hyperbolic systems
35L71 Second-order semilinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35R09 Integro-partial differential equations
35Q74 PDEs in connection with mechanics of deformable solids
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