Stability of the interface between two immiscible fluids in porous media.
In questa Nota, che è il seguito della Nota precedente, proseguiamo lo studio del problema di equilibrio di un involucro elastico pieno di gas, considerando piccole perturbazioni di una configurazione di equilibrio, prodotte da insufflazioni o desufflazioni di piccole quantità di gas. Limitando la nostra attenzione al caso che l'involucro sia una corona sferica che subisce solo deformazioni radiali, mostriamo che, per un valore critico dello spessore della corona, il carattere non locale delle condizioni...
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.
The purpose of this paper is to study a model coupling an incompressible viscous fiuid with an elastic structure in a bounded container. We prove the existence of weak solutions à la Leray as long as no collisions occur.