caa a22 4500 445329912 CHVBK 20180317142734.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00285-010-0379-z doi (NATIONALLICENCE)springer-10.1007/s00285-010-0379-z Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation [Elektronische Daten] [Shantia Yarahmadian, Blake Barker, Kevin Zumbrun, Sidney Shaw] We generalize the Dogterom-Leibler model for microtubule dynamics (Dogterom and Leibler in Phys Rev Lett 70(9):1347-1350, 1993) to the case where the rates of elongation as well as the lifetimes of the elongating shortening phases are a function of GTP-tubulin concentration. We analyze 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. Springer-Verlag, 2010 Yarahmadian Shantia Mississippi State University, 39762, Mississippi State, MS, USA aut Barker Blake Indiana University, 47405, Bloomington, IN, USA aut Zumbrun Kevin Indiana University, 47405, Bloomington, IN, USA aut Shaw Sidney Indiana University, 47405, Bloomington, IN, USA aut Journal of Mathematical Biology Springer-Verlag 63/3(2011-09-01), 459-492 0303-6812 63:3<459 2011 63 285 https://doi.org/10.1007/s00285-010-0379-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0379-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yarahmadian Shantia Mississippi State University, 39762, Mississippi State, MS, USA aut NATIONALLICENCE 700 1- Barker Blake Indiana University, 47405, Bloomington, IN, USA aut NATIONALLICENCE 700 1- Zumbrun Kevin Indiana University, 47405, Bloomington, IN, USA aut NATIONALLICENCE 700 1- Shaw Sidney Indiana University, 47405, Bloomington, IN, USA aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/3(2011-09-01), 459-492 0303-6812 63:3<459 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer