Existence and linear stability of solutions       of the ballistic VSC model

Joost Hulshof; Robert Nolet; Georg Prokert

doi:10.3934/dcdss.2014.7.35

Article Contents

2014, Volume 7, Issue 1: 35-51. Doi: 10.3934/dcdss.2014.7.35

This issue Previous Article A thermohydraulics model with temperature dependent constraint on velocity fields Next Article Crystalline motion of spiral-shaped polygonal curves with a tip motion

Existence and linear stability of solutions of the ballistic VSC model

1.
VU University Amsterdam, Faculty of Sciences, De Boelelaan 1081, 1081 HV Amsterdam
2.
TU Eindhoven, Faculty of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven

Received: February 2012

Revised: March 2013

Published online: July 2013

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Abstract

An equation for the dynamics of the vesicle supply center model of tip growth in fungal hyphae is derived. For this we analytically prove the existence and uniqueness of a traveling wave solution which exhibits the experimentally observed behavior. The linearized dynamics around this solution is analyzed and we conclude that all eigenmodes decay in time. Numerical calculation of the first eigenvalue gives a timescale in which small perturbations will die out.

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Mathematics Subject Classification: Primary: 35Q92; Secondary: 92C37, 35C07.

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