Solvability in Hölder spaces of an integral equation which models dynamics of the capillary rise

Abstract

In this paper, we focus on an integral equation which allows us to model the dynamics of the capillary rise of a fluid inside a tubular column. Using Schauder's fixed-point theorem, we prove that such integral equation has at least one solution in the Hölder space H1[0,b], where b>0. Moreover, we are able to prove the uniqueness of the solution under certain conditions. Our results extend the ones obtained in earlier works (see [5]).