Vibrational stabilization and transient behavior analysis of nonlinear parabolic systems with Neumann boundary conditions

Conditions for the existence of stabilizing vibrations are derived for a class of distributed-parameter systems governed by parabolic partial differential equations with Neumann boundary conditions. Guidelines for the choice of the vibration parameters that ensure stabilization are given. The transient behavior of vibrationally controlled systems is also studied. Examples of vibrational stabilization of unstable systems by linear multiplicative and vector additive vibrations are given to support the theory.<>