The method of adapted energies for second order evolution equations with dissipation (Q6144003)

Summary: This survey paper emphasizes the method of adapted energy functions to obtain sharp information on various stability questions: exponential stability, strong stability with explicit decay rates, ultimate bounds of solutions and so on. The efficiency of the method, basically related to Lyapunov's and Barbashin-Krasovskii-LaSalle's approaches, very often allows one to obtain close-to-optimal estimates, as demonstrated on a variety of examples connected to mechanics via differential equations of second order with respect to the time variable. For the entire collection see [Zbl 1504.74002].