Abstract
The Cauchy problem for a quasi-linear degenerate parabolic equation in divergence from with energy space , , , and with initial function is considered. The existence of a generalized solution is proved for growing at infinity at the rate: For more sever constraints on the growth of several fairly wide uniqueness classes for the above-mentioned solution are discovered. The question of describing the geometry of the domain for is considered. In case when the domain is unbounded, estimates in terms of the global properties of the initial function are established that characterize the geometry of as .
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