  We consider the unnormalized Yamabe flow on manifolds with conical
singularities. Under certain geometric assumption on the initial cross-section
we show well posedness of the short time solution in the $L^q$-setting.
Moreover, we give a picture of the deformation of the conical tips under the
flow by providing an asymptotic expansion of the evolving metric close to the
boundary in terms of the initial local geometry. Due to the blow up of the
scalar curvature close to the singularities we use maximal $L^q$-regularity
theory for conically degenerate operators.
