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We have considered the dislocation network model for the supersolid state inHe-4 crystals. In difference with uniform 2D and 3D systems, the temperature ofsuperfluid transition T_c in the network is much smaller than the degeneracytemperature T_d. It is shown that a crossover into a quasi superfluid stateoccurs in the temperature interval between T_c and T_d. Below the crossovertemperature the time of decay of the flow increases exponentially underdecrease of the temperature. The crossover has a continuous character and thecrossover temperature does not depend on the density of dislocations.

Relaxation of superflow in a network: an application to the dislocation model of supersolidity of helium crystals