We study the energy decay of the difference of two solutions for dissipativ
e evolution problems of the type:
u " + Lu + g(u') = h(t), t greater than or equal to 0,
including wave and plate equations and ordinary differential equations. In
the general case, when the damping term g behaves like a power of the veloc
ity u', the energy decreases like a negative power of time, multiplied by a
constant depending on the initial energies. We provide estimates on these
constants and prove their optimality. In the special case of the ordinary d
ifferential equation with periodic forcing, we establish, relying on a cont
rollability-like technique, that the decay is in fact exponential, even und
er very weak damping.