Existence and energy decay rates of solutions to the variable-coefficient Euler-Bernoulli plate with a delay in localized nonlinear internal feedback. (English) Zbl 1343.93065
Summary: This paper is concerned with the existence and energy decay estimates of solutions to the variable-coefficient Euler-Bernoulli plate with a delay in localized nonlinear internal feedback. The existence of solutions to the nonlinear system is obtained by using Galerkin method combined with some energy estimates. Furthermore, applying Riemannian geometry method, we establish uniform decay rates of the plate equation with variable coefficients and a nonlinear delay term.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 74K20 | Plates |
| 35L76 | Higher-order semilinear hyperbolic equations |
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
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