ASYMPTOTIC BEHAVIOR OF THE LINEARIZED COMPRESSIBLE BAROTROPIC NAVIER-STOKES SYSTEM WITH A TIME VARYING DELAY TERM IN THE BOUNDARY OR INTERNAL FEEDBACK - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

ASYMPTOTIC BEHAVIOR OF THE LINEARIZED COMPRESSIBLE BAROTROPIC NAVIER-STOKES SYSTEM WITH A TIME VARYING DELAY TERM IN THE BOUNDARY OR INTERNAL FEEDBACK

Résumé

In this paper, we consider the linearized compressible barotropic Navier-Stokes system in a bounded interval (0, L) with a time-varying delay term in the Dirichlet boundary or internal feedback of the hyperbolic component. Assuming some suitable conditions on the time-dependent delay term and the coefficients of feedback (delayed or not), we study the exponential stability of the concerned hyperbolicparabolic system. Due to the presence of the time-varying delay term, the corresponding spatial operator is also time-dependent. Using classical semigroup theory with Kato's variable norm approach, we first show the existence and uniqueness of the Navier-Stokes system with time delay, acting in the boundary or interior. Next, we prove the two stabilization results by means of interior delay feedback and boundary delay. In both cases, we establish the exponential stability results by introducing some suitable functional energy and using the Lyapunov function approach.
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Dates et versions

hal-03910235 , version 1 (21-12-2022)
hal-03910235 , version 2 (26-06-2023)

Identifiants

  • HAL Id : hal-03910235 , version 2

Citer

Subrata Majumdar. ASYMPTOTIC BEHAVIOR OF THE LINEARIZED COMPRESSIBLE BAROTROPIC NAVIER-STOKES SYSTEM WITH A TIME VARYING DELAY TERM IN THE BOUNDARY OR INTERNAL FEEDBACK. 2023. ⟨hal-03910235v2⟩
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