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Optimal decay rates and asymptotic profile for the plate equation with structural damping. (English) Zbl 1339.35043

Summary: In this work we study decay rates for the \(L^2\)-norm of solutions to the plate equation with fractional damping and a pseudo fractional rotational inertia term. We also show that the decay rates depending on the fractional power of the damping term are optimal using an asymptotic expansion of the corresponding solution of the related equation in the Fourier space.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
74K20 Plates
35R11 Fractional partial differential equations
35L35 Initial-boundary value problems for higher-order hyperbolic equations
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