Large time behavior of solutions to degenerate parabolic equations with absorption

We study existence, uniqueness, and large time behavior of positive classical solutions of the Dirichlet initial-boundary value problem for the equation¶\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ u_t = u^p \Delta u - u^q $\end{document}¶ with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ p, q \ge 1 $\end{document}. Decay rates and asymptotic profiles are discussed.