  We consider a second order linear evolution equation with a dissipative term
multiplied by a time-dependent coefficient. Our aim is to design the
coefficient in such a way that all solutions decay in time as fast as possible.
  We discover that constant coefficients do not achieve the goal, as well as
time-dependent coefficients that are too big. On the contrary, pulsating
coefficients which alternate big and small values in a suitable way prove to be
more effective.
  Our theory applies to ordinary differential equations, systems of ordinary
differential equations, and partial differential equations of hyperbolic type.

Analysis of PDEs