It has long been established that gradients in the Alfvén speed, and in particular the plasma
density, are an essential part of the damping of waves in the magnetically closed solar corona
by mechanisms such as resonant absorption or phase mixing. While models of wave damping
often assume a fixed density gradient, in this paper the self-consistency of such calculations
is assessed by examining the temporal evolution of the coronal density. It is shown
conceptually that for some coronal structures, density gradients can evolve in a way that the
wave damping processes are inhibited. For the case of phase mixing we argue that: (a) wave
heating cannot sustain the assumed density structure and (b) inclusion of feedback of the
heating on the density gradient can lead to a highly structured density, although on long
timescales. In addition, transport coefficients well in excess of classical are required to
maintain the observed coronal density. Hence, the heating of closed coronal structures by
global oscillations may face problems arising from the assumption of a fixed density gradient
and the rapid damping of oscillations may have to be accompanied by a separate (non-wave
based) heating mechanism to sustain the required density structuring.