Propagation of support in one-dimensional convected thin-film flow Lorenzo GiacomelliAndrey Shishkov 35B9935G2535K3035K6535Q3535R3576D0876D27Finite speed of propagationnonlinear higher-order PDEdegenerate parabolic equationsthin-film equationsconvection-diffusion equationsfree boundary problemslubrication theory In one space dimension, we study the finite speed of propagation property for zero contact-angle solutions of the thin-film equation in presence of a convective term. In the case of strong slippage, we obtain bounds in terms of the initial mass for both the ``fast'' and the ``slow'' interfaces, and for both short and (whenever the solution is global) large times, which we expect to be sharp. In the case of weak slippage, we obtain partial results for short times, which include a quantitative bound for moderate growths of the convective term. Our approach is based on energy/entropy methods shaped upon suitable extensions of Stampacchia's Lemma. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2532 10.1512/iumj.2005.54.2532 en Indiana Univ. Math. J. 54 (2005) 1181 - 1216 state-of-the-art mathematics http://iumj.org/access/