# H. Essaouini, L. El Bakkali and P. Capodanno, Analysis of the Small Oscillations of a Heavy Inviscid Liquid in a Container Supported by an Elastic Structure, Volume 2017, Number 5, Pages 1-11, 2017

**Abstract: **The authors propose a mathematical study of the small oscillations of a heavy inviscid liquid in an arbitrary rigid container supported by an elastic structure. From the equations of motion of the system, they deduce a variational formulation of the problem and after, an operatorial equation in a suitable Hilbert space. Then, they can study the spectrum of the problem:they prove that it is formed by eigenvalues that are located in the left half-plane, so that the equilibrium position is stable. Moreover, they show that the operator pencil of the problem can be considered as a weakly damped Krein-Langer pencil, so that they can prove that the eigenmotions are oscillatory and precise the location of the eigenvalues. Finally, they prove the existence and the unicity of the solution of the associated evolution problem by means of the semi-groups theory.

**Keywords:** Small oscillations, Variational, Operatorial and spectral methods, Semi-groups theory.

**How to cite this article: **

H. Essaouini, L. El Bakkali and P. Capodanno, Analysis of the Small Oscillations of a Heavy Inviscid Liquid in a Container Supported by an Elastic Structure, International Journal of Advances in Mathematics, Volume 2017, Number 5, Pages 1-11, 2017.