Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity. (English) Zbl 1400.35177
Summary: In this paper, we consider a viscoelastic plate equation with a logarithmic nonlinearity. Using the Galaerkin method and the multiplier method, we establish the existence of solutions and prove an explicit and general decay rate result. This result extends and improves many results in the literature such as [P. Górka, Acta Phys. Pol. B 40, No. 1, 59–66 (2009; Zbl 1371.81101); T. Hiramatsu et al., “Numerical study of Q-ball formation in gravity mediation”, J. Cosmol. Astropart. Phys. 2010, No. 6, Paper No. 8, 28 p. (2010; doi:10.1088/1475-7516/2010/06/008); X. Han and M. Wang, Acta Appl. Math. 110, No. 1, 195–207 (2010; Zbl 1194.35060)].
MSC:
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
| 35B35 | Stability in context of PDEs |
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 93D20 | Asymptotic stability in control theory |
| 74K20 | Plates |
| 35R09 | Integro-partial differential equations |
| 35L76 | Higher-order semilinear hyperbolic equations |
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