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Polynomial stability of operator semigroups. (English) Zbl 1118.47034
The authors study the polynomial decay of classical solutions of linear evolution equations. For bounded strongly continuous semigroup on a Banach space, this property is closely related to polynomial growth estimates of the resolvent of the generator. For systems of commuting normal operators, polynomial decay is characterized in terms of the location of the generator spectrum. The results are applied to systems of coupled wave-type equations.

MSC:
47D06 One-parameter semigroups and linear evolution equations
34G10 Linear differential equations in abstract spaces
35B40 Asymptotic behavior of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
35P15 Estimates of eigenvalues in context of PDEs
47A10 Spectrum, resolvent
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