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Generation of a Semigroup and Hidden Regularity in Nonlinear Subsonic Flow-Structure Interactions with Absorbing Boundary Conditions

Volume 3, Number 1 (2012), 1 - 27

Generation of a Semigroup and Hidden Regularity in Nonlinear Subsonic Flow-Structure Interactions with Absorbing Boundary Conditions

Communicated By: 
Alain Haraux
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Abstract

PDE evolutionary model arising in a flow-structure interaction with a subsonic velocity of the flow and absorbing boundary conditions is considered. It is shown that the underlying PDE system generates a strongly continuous semigroup which is associated with finite energy solutions. This result depends on ”hidden regularity” estimate displayed by boundary traces of the solutions. It is shown that the sequence of semigroups corresponding to absorbing boundary conditions has a strong limit when the absorbtion parameter goes to zero. This limit allows to define a semigroup that corresponds to the model with conservative boundary conditions where the hidden boundary regularity is lost in the limit.