In the cosmic web, galaxy superclusters or their high-density cores are the largest objects that may collapse at present or during the future evolution. We study the dynamical state and possible future evolution of galaxy superclusters from the Sloan Great Wall (SGW), the richest galaxy system in the nearby Universe. We calculated supercluster masses using dynamical masses of galaxy groups and stellar masses of galaxies. We employed normal mixture modelling to study the structure of rich SGW superclusters and search for components (cores) in superclusters. We analysed the radial mass distribution in the high-density cores of superclusters centred approximately at rich clusters and used the spherical collapse model to study their dynamical state. We found that the lower limit of the total mass of the SGW is approximately $M = 2.5times~10^{16}h^{-1}M_odot$. Different mass estimators of superclusters agree well, the main uncertainties in masses of superclusters come from missing groups and clusters. We detected three high-density cores in the richest SGW supercluster (SCl~027) and two in the second richest supercluster (SCl~019). They have masses of $1.2 - 5.9 times~10^{15}h^{-1}M_odot$ and sizes of up to $approx 60 h^{-1}$ Mpc. The high-density cores of superclusters are very elongated, flattened perpendicularly to the line of sight. The comparison of the radial mass distribution in the high-density cores with the predictions of spherical collapse model suggests that their central regions with radii smaller than $8 h^{-1}$Mpc and masses of up to $M = 2times~10^{15}h^{-1}M_odot$ may be collapsing. The rich SGW superclusters with their high-density cores represent dynamically evolving environments for studies of the properties of galaxies and galaxy systems.
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