Existence and linear stability of solutions of the ballistic VSC model

J. Hulshof; R. Nolet; G. Prokert

doi:10.3934/dcdss.2014.7.35

Existence and linear stability of solutions of the ballistic VSC model

J. Hulshof
, R. Nolet
, G. Prokert

Research output: Contribution to journal › Article › Academic › peer-review

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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. Keywords: Fungal hyphae, cell growth, traveling wave, linear stability, free boundary problem.

Original language	English
Pages (from-to)	35-51
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	7
Issue number	1
DOIs	https://doi.org/10.3934/dcdss.2014.7.35
Publication status	Published - 2014

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title = "Existence and linear stability of solutions of the ballistic VSC model",

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. Keywords: Fungal hyphae, cell growth, traveling wave, linear stability, free boundary problem.",

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AU - Hulshof, J.

AU - Nolet, R.

AU - Prokert, G.

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N2 - 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. Keywords: Fungal hyphae, cell growth, traveling wave, linear stability, free boundary problem.

AB - 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. Keywords: Fungal hyphae, cell growth, traveling wave, linear stability, free boundary problem.

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DO - 10.3934/dcdss.2014.7.35

M3 - Article

SN - 1937-1632

VL - 7

SP - 35

EP - 51

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 1

ER -

Existence and linear stability of solutions of the ballistic VSC model

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