Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation

Details Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation

2010-04-12

arxiv.org/abs/1004.1866v1

Mathematics

Analysis of PDEs

Scientific paper

We generalize the Dogterom-Leibler model for microtubule dynamics [DL] to the case where the rates of elongation as well as the lifetimes of the elongating and shortening phases are a function of GTP-tubulin concentration. We study also the effect of nucleation rate in the form of a damping term which leads to new steady-states. For this model, we study existence and stability of steady states satisfying the boundary conditions at x = 0. Our stability analysis introduces numerical and analytical Evans function computations as a new mathematical tool in the study of microtubule dynamics.

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