Asymptotic behavior of regularized shock solutions in coating flows
Academic Article

Overview

Research

View All

Overview

abstract

We consider a model for thin liquid films in a rotating cylinder in the small
surface tension limit. Using dynamical system methods, we show that the
continuum of increasing shock solutions persists in the small surface tension
limit, whereas the continuum of decreasing shock solutions terminates at the
limit. Using delicate numerical computations, we show that the existence curves
of regularized shock solutions on the mass-flux diagram exhibit loops. The
number of loops increases and their locations move to infinity as the surface
tension parameter decreases to zero. If $n$ is the number of loops in the
mass-flux diagram with $2n+1$ solution branches, we show that $n+1$ solution
branches are stable with respect to small perturbations.