Transient behavior analysis of vibrationally controlled nonlinear parabolic systems with Neumann boundary conditions

The transient behavior of vibrationally controlled distributed parameter systems governed by parabolic partial differential equations (PDEs) with Neumann boundary conditions is analyzed. The analysis uses a certain mapping and a time-invariant PDE whose trajectories under this mapping yield the approximate moving averages along the trajectories of the vibrationally controlled system. This approach considerably enhances the understanding of the behavior of vibrationally controlled distributed-parameter systems and facilitates a selection of the parameters of stabilizing vibrations that ensure transient behavior with more desirable properties