We study the stability of a thin membrane (of zero bending rigidity) with vortex sheet as nonlinear eigenvalue problem in parameter space mass (${R}_{1}$) and pretension (${T}_{0}$). With both ends fixed light membranes become unstable by divergence instability heavy lose flutter for ${T}_{0}$ that increases ${R}_{1}$. leading edge trailing free, or edges eigenmodes transition shape across boun...

We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. Though this model can be considered simple, its mathematical analysis i...