On a New Family of Degenerate Parabolic Equations

Abstract

which was first derived in (Ulusoy, Nonlinearity 20 (2007): 685–712). We prove results on the regularity of non-negative solutions. In Ulusoy, an entropy dissipation–entropy estimate was provided for the p = 3 and n = 2 case using the energy functional Kq := ∫ hx hq dx. Here, we extend our calculations to include various other p and n values. After establishing some results on the support properties of solutions, we finally complete the analysis of the long-time behavior of non-negative weak solutions.