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We investigate the convergence of solutions of a recently proposed diffuseinterface/phase field model for cell blebbing by means of matched asymptoticexpansions. It is a biological phenomenon that increasingly attracts attentionby both experimental and theoretical communities. Key to understanding theprocess of cell blebbing mechanically are proteins that link the cell cortexand the cell membrane. Another important model component is the bending energyof the cell membrane and cell cortex which accounts for differential equationsup to sixth order. Both aspects pose interesting mathematical challenges thatwill be addressed in this work like showing non-singularity formation for thepressure at boundary layers, deriving equations for asymptotic seriescoefficients of uncommonly high order, and dealing with a highly coupled systemof equations.

Sharp interface analysis of a diffuse interface model for cell blebbing with linker dynamics