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

Akram Ben Aissa (1) , Mama Abdelli (2) , Alessandro Duca (3)

1 UM - Université de Monastir - University of Monastir
2 UDL - جامعة جيلالي اليابس [سيدي بلعباس، الجزائر] = Université Djillali Liabès [Sidi Bel Abbès, Algérie] = Djillali Liabes University [Sidi Bel Abbès, Algeria]
3 IF - Institut Fourier

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. 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.

Mots clés: Beam; Lyapunov’s direct method; Uniform stability; Exponential stability; Internal fluid

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]; Théorie spectrale [math.SP]

Akram Ben Aissa, Mama Abdelli, Alessandro Duca. WELL-POSEDNESS AND EXPONENTIAL DECAY FOR THE EULER-BERNOULLI BEAM CONVEYING FLUID EQUATION WITH NON-CONSTANT VELOCITY AND DYNAMICAL BOUNDARY CONDITIONS. Zeitschrift für Angewandte Mathematik und Physik, 2021. ⟨hal-02570702v2⟩