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

  title={Well-Posedness and Self-Similar Asymptotics for a Thin-Film Equation},
  author={Manuel V. Gnann},
  journal={SIAM J. Math. Analysis},
We investigate compactly supported solutions for a 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 for the corresponding classical free boundary problem and set up a global existence and uniqueness theory… CONTINUE READING