WELL-POSEDNESS AND EXPONENTIAL DECAY FOR THE EULER-BERNOULLI BEAM CONVEYING FLUID EQUATION WITH NON-CONSTANT VELOCITY AND DYNAMICAL BOUNDARY CONDITIONS - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2020

WELL-POSEDNESS AND EXPONENTIAL DECAY FOR THE EULER-BERNOULLI BEAM CONVEYING FLUID EQUATION WITH NON-CONSTANT VELOCITY AND DYNAMICAL BOUNDARY CONDITIONS

Résumé

In this paper, we consider an Euler-Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving with non-constant velocity and dynamical boundary conditions are satisfied. By using a semigroup approach, we prove the existence and uniqueness of global solution under suitable assumptions on the tension of beam and on the parameters of the problem. Afterwards, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
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Dates et versions

hal-02570702 , version 1 (12-05-2020)
hal-02570702 , version 2 (30-10-2020)

Identifiants

  • HAL Id : hal-02570702 , version 1

Citer

Alessandro Duca, Mama Abdelli, Akram Ben Aissa. WELL-POSEDNESS AND EXPONENTIAL DECAY FOR THE EULER-BERNOULLI BEAM CONVEYING FLUID EQUATION WITH NON-CONSTANT VELOCITY AND DYNAMICAL BOUNDARY CONDITIONS. 2020. ⟨hal-02570702v1⟩
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