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| goes to infinity 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 S and in its dual space S'.
The global Cauchy problem for the plate equation in weighted Sobolev spaces
Ascanelli A.
Primo
2020
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| goes to infinity 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 S and in its dual space S'.File in questo prodotto:
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