Stabilization of solutions of dissipative Hamiltonian systems (Q536279)

This article deals with stabilization of solutions of damped Hamiltonian systems. It is well-known that stabilization is not possible for general gradient systems, and there are counterexamples which show that also for infinite-dimensional Hamiltonian systems, one cannot expect stabilization in general. The authors provide a sufficient condition for stabilization, which is given by a so-called Łojasiewicz-Simon inequality for the Hamiltonian. Decay estimates are given, and many examples illustrate the theoretical findings.