Source Type Solutions of a Fourth Order Degenerate Parabolic Equation (Journal of Partial Differential Equations, 2009)
In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 < n < 2p-1 and has no solution of this type if n ≥ 2p-1.