we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

in this paper we consider a petrovsky viscoelastic inverse source problem with memory term in the boundary condition. we obtain sufficient conditions on relaxation function and initial data for which the solutions of problem are asymptotically stable when the integral overdetermination tends to zero as time goes to infinity.