ANALYTICAL AND NUMERICAL RESULTS ON THE POSITIVITY OF STEADY STATE SOLUTIONS OF A THIN FILM EQUATION

Abstract. We consider an equation for a thin-film of fluid on a rotating cyl-inder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and clas-sical steady states must be strictly positive so long as the speed of rotation is nonzero. Next, we formulate a novel spectral iteration algorithm for com-puting these steady states. Finally, we explore a non-existence inequality for steady state solutions from the recent work of Chugunova, Pugh, & Taranets. 1