TY - JOUR
AU - R. M. Taranets
PY - 2019/06/25
Y2 - 2020/11/27
TI - Finite speed of propagation for the thin-film equation in the spherical geometry
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 71
IS - 6
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1479
AB - UDC 517.953 We show that a double degenerate thin-film equation obtained in modeling of a flow of viscous coating on the spherical surface has a finite speed of propagation for nonnegative strong solutions and, hence, there exists an interface or a free boundary separating the regions, where the solution $u>0$ and $u=0.$ Using local entropy estimates, we also obtain the upper bound for the rate of the interface propagation.
ER -