Well-Posedness and Self-Similar Asymptotics for a Thin-Film Equation

We investigate compactly supported solutions for the thin-film equation with linear mobility in the regime of perfect wetting. This problem has already been addressed by Carrillo and Toscani, proving that the source-type self-similar profile is a global attractor of entropy solutions with compactly supported initial data. Here we study small perturbations of source-type self-similar solutions and set up a global existence and uniqueness theory within weighted L2-spaces. As spatial translations are scaled out in our reference frame, the rate of convergence is higher than the one obtained by Carrillo and Toscani.