  We have re-examined the Andreev-Lifshitz theory of supersolids. This theory
implicitly neglects uniform bulk processes that change the vacancy number, and
assumes an internal pressure $P$ in addition to lattice stress $\lambda_{ik}$.
Each of $P$ and $\lambda_{ik}$ takes up a part of an external, or applied,
pressure $P_a$ (necessary for solid 4He). The theory gives four pairs of
propagating elastic modes, of which one pair corresponds to a fourth-sound
mode, and a single diffusive mode, which has not been analyzed previously. The
diffusive mode has three distinct velocities, with the superfluid velocity much
larger than the normal fluid velocity, which in turn is much larger than the
lattice velocity. The mode structure depends on the relative values of certain
kinetic coefficients and thermodynamic derivatives. We consider pressurization
experiments in solid 4He at low temperatures in light of this diffusion mode
and a previous analysis of modes in a normal solid with no superfluid
component.
