Global existence for two singular one-dimensional nonlinear viscoelastic equations with respect to distributed delay term. (English) Zbl 1462.35193
Summary: In this current work, we are interested in a system of two singular one-dimensional nonlinear equations with a viscoelastic, general source and distributed delay terms. The existence of a global solution is established by the theory of potential well, and by using the energy method with the function of Lyapunov, we prove the general decay result of our system.
MSC:
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35L81 | Singular hyperbolic equations |
| 35R09 | Integro-partial differential equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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