On the detection of a moving obstacle in an ideal fluid by a boundary measurements

On the detection of a moving obstacle in an ideal fluid by a boundary measurements

Inverse problems in fuid mechanics constitute a challenging topic with numerous potential applications, ranging from engineering, medicine, and military surveillance to fishing.
In this case we are interested in to study the existence and uniqueness of a model which describe the dynamic of a fuid-solid system, in particular the fuid considered is non viscous and the dynamic of the solid B(t) is due to its interaction with the fuid.

Firstly we will discuss the existence and uniqueness of solutions of the model which describe this system when the fuids fulfills an unbounded region R2 \ B(t). Later we will discuss the existence and uniqueness when the fuid f fulfills a bounded region Ω(t) = Ω\ B(t)

Finally, we study the problem of obtain some information about the solid through the observation of the velocity at some part Γ of the exterior boundary ∂Ω. To do this, firstly we analyze the wellposedness of the problem and we obtain the determination of the position and the velocity of the obstacle from a boundary measurement of the velocity of the fuid at a given time t. Some numerical results will be presented.