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Decay rates for solutions of damped systems and generalized Fourier transforms. (English) Zbl 0718.35015
L\({}^ p-L^ q\) decay estimates for solutions of damped systems like the damped wave equation with variable coefficients or a fourth order parabolic equation are proved for exterior domains with star-shaped resp. convex complement. A generalized eigenfunction expansion is used and pointwise estimates on the associated Fourier kernel are presented.
Reviewer: Reinhard Racke

35B40 Asymptotic behavior of solutions to PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35K35 Initial-boundary value problems for higher-order parabolic equations
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