Existence of solutions to the diffusive VSC model

J. Hulshof, R.W. Nolet, G. Prokert

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We prove existence of classical solutions to the so-called diffusive vesicle supply center (VSC) model describing the growth of fungal hyphae. It is supposed in this model that the local expansion of the cell wall is caused by a flux of vesicles into the wall and that the cell wall particles move orthogonally to the cell surface. The vesicles are assumed to emerge from a single point inside the cell (the VSC) and to move by diffusion. For this model, we derive a nonlinear, nonlocal evolution equation and show the existence of solutions relevant to our application context, namely, axially symmetric surfaces of fixed shape, traveling along with the VSC at constant speed. Technically, the proof is based on the Schauder fixed point theorem applied to Holder spaces of functions. The necessary estimates rely on comparison and regularity arguments from elliptic PDE theory. © 2013 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)700-727
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume45
Issue number2
DOIs
Publication statusPublished - 2013

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