Polynomial semigroup stability implies periodic well-posedness on a dense set of forcings whose time-derivative loss is controlled by resolvent bounds.
Wehbe, Rational energy decay rate for a wave equation with dynamical control, Appl
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From Polynomial Stability to Periodic Well-posedness in Partially Dissipative Systems
Polynomial semigroup stability implies periodic well-posedness on a dense set of forcings whose time-derivative loss is controlled by resolvent bounds.