Facet bending driven by the planar crystalline curvature with a generic nonuniform forcing term

We study crystalline driven curvature flow with spatially nonuniform driving force term. We assume special monotonicity properties of the driving term, which are motivated by our previous work on Berg's effect. We consider special initial data which we call ‘bent rectangles.’ We prove existence of solutions for a generic forcing term as well as generic subclass of bent rectangles. We show the initially flat facets may begin to bend, provided, loosely speaking, they are too large. Moreover, depending on the initial configuration we notice instantaneous loss of regularity of the moving curve.