Decay estimates to equilibrium for some asymptotically autonomous semilinear evolution equations

We estimate the rate of decay of the difference between a solution and its limiting equilibrium for the nonautonomous first-order problem

u˙+ℳu=g(t),  t∈R₊ ,

and for the second-order problem

u¨+u˙+ℳu=g(t),  t∈R₊,

where ℳ is a gradient operator and g is a function which tends to 0 when t tends to ∞.