The Cauchy problem for a degenerate parabolic equation with inhomogeneous density and source in the class of slowly decaying initial data

Given a degenerate parabolic equation of the form with a source and inhomogeneous density, we consider the Cauchy problem with an initial function slowly tending to zero as . We find conditions for the global-in-time existence or non-existence of solutions of this problem. These conditions depend essentially on the behaviour of the initial data as . In the case of global solubility we obtain a sharp estimate of the solution for large values of time.

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