  We investigate the convergence of solutions of a recently proposed diffuse
interface/phase field model for cell blebbing by means of matched asymptotic
expansions. It is a biological phenomenon that increasingly attracts attention
by both experimental and theoretical communities. Key to understanding the
process of cell blebbing mechanically are proteins that link the cell cortex
and the cell membrane. Another important model component is the bending energy
of the cell membrane and cell cortex which accounts for differential equations
up to sixth order. Both aspects pose interesting mathematical challenges that
will be addressed in this work like showing non-singularity formation for the
pressure at boundary layers, deriving equations for asymptotic series
coefficients of uncommonly high order, and dealing with a highly coupled system
of equations.
