In this paper we show that a universe dominated by two components, namely domain walls and dissipative dark matter such that the former slowly decays into the latter may drive power law cosmological acceleration consistent with the high redshift supernovae data, while the ratio between the energy densities of both components remains fixed at late times thus solving the coincidence problem of present acceleration. Likewise, we estimate the aforesaid ratio at early times.

15 pages, 2 eps figures, uses revtex4, to be published in Physical Review D