We present new sub-arcsecond (0.7) Combined Array for Research in Millimeter-wave Astronomy (CARMA) observations of the 1.3 mm continuum emission from circumstellar disks around 11 low and intermediate mass pre-main sequence stars. High resolution observations for 3 additional sources were obtained from literature. In all cases the disk emission is spatially resolved. We adopt a self consistent accretion disk model based on the similarity solution for the disk surface density and constrain the dust radial density distribution on spatial scales of about 40 AU. Disk surface densities appear to be correlated with the stellar ages where the characteristic disk radius increases from ~ 20 AU to 100 AU over about 5 Myr. This disk expansion is accompanied by a decrease in the mass accretion rate, suggesting that our sample disks form an evolutionary sequence. Interpreting our results in terms of the temporal evolution of a viscous $alpha$-disk, we estimate (i) that at the beginning of the disk evolution about 60% of the circumstellar material was located inside radii of 25--40 AU, (ii) that disks formed with masses from 0.05 to 0.4 M$_{sun}$ and (iii) that the viscous timescale at the disk initial radius is about 0.1-0.3 Myr. Viscous disk models tightly link the surface density $Sigma(R)$ with the radial profile of the disk viscosity $ u(R) propto R^{gamma}$. We find values of $gamma$ ranging from -0.8 to 0.8, suggesting that the viscosity dependence on the orbital radius can be very different in the observed disks. Adopting the $alpha$ parameterization for the viscosity, we argue that $alpha$ must decrease with the orbital radius and that it may vary between 0.5 and $10^{-4}$. (abridged)
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