A conditional stability criterion based on generalized energies

An energy criterion for conditional stability is proposed, based on the definition of generalized energies, obtained through a perturbation of the classical L2 (kinetic) energy. This perturbation is such that the contribution of the linear term in the perturbation equation to the generalized energy time derivative is negative definite. A critical amplitude threshold is then obtained by imposing the monotonic decay of the generalized energy. The capabilities of the procedure are appraised through the application to three different low-dimensional models. The effects of different choices in the construction of the generalized energy on the prediction of the critical amplitude threshold in the subcritical regime are also discussed.