Abstract
We consider the initial value problem for the plate equation with (t, x) −depending complex valued lower order terms. Under suitable decay conditions as |x|→∞ on the imaginary part of the subprincipal term we prove energy estimates in weighted Sobolev spaces. This provides also well posedness of the Cauchy problem in the Schwartz space \(\mathcal {S}(\mathbb R^n)\) and in \(\mathcal {S}^\prime (\mathbb R^n)\).
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Ascanelli, A. (2020). The Global Cauchy Problem for the Plate Equation in Weighted Sobolev Spaces. In: Boggiatto, P., et al. Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36138-9_3
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DOI: https://doi.org/10.1007/978-3-030-36138-9_3
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