Exponential asymptotics and problems with coalescing singularities

摘要: Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion form a factorial divided power. In this paper, we demonstrate that certain classes problems involve coalescing singularities, more general type exponential-over-power must be used. As model example, study water waves produced flow past an obstruction such as surface-piercing ship. low speed or Froude limit, resultant exponentially small, and their formation is attributed to singularities geometry obstruction. However, cases where closely spaced, usual theory fails. We present both framework for handling provide numerical results particular examples.