Evolution of Nonparametric Surfaces with Speed Depending on Curvature Function

Abstract

We investigate the asymptotic behaviour of solution of the initial-boundary value problem for the equation, which describes the evolution of graphs with speed depending on curvature function of current graphs. In contrast with [1-5] and others, in which the speed of flow of graphs is directly proportional to the curvature of graphs, here we discuss is that the speed is inversely proportional to the curvature of graphs, and our methods is different from theirs.