Doubly degenerate parabolic equation with time-dependent gradient source and initial data measures (Q2301587)

The authors prove the existence of nonnegative solutions of a Cauchy problem intensively investigated in the last decades. In particular, it has been proposed as an appropriate model for surface growth by ballistic deposition and specifically for vapour deposition and the sputter deposition of thin films of aluminium and rare earth metals. The Cauchy problem is related to a class of doubly degenerate parabolic equation with time-dependent gradient source, where the initial data are Radon measures. The considered equation is of a class of non-Newtonian polytropic filtration equation, it contains the heat equation, the porous medium equation, the evolutionary \(p\)-Laplacian equation and others. Gradient estimates and \(L^\infty\)-estimates of solutions Gagliardo-Nirenberg inequality and Young's inequality are the main basic tools to get the conclusion.