@article{e6e7f0c6e5244862b5f6a6d69a89ca28,
title = "Traveling waves of a go-or-grow model of glioma growth",
abstract = "Glioblastoma multiforme is a deadly brain cancer in which tumor cells excessively proliferate and migrate. The first mathematical models of the spread of gliomas featured reaction-diffusion equations, and later an idea emerged through experimental study called the {"}Go or Grow{"} hypothesis in which glioma cells have a dichotomous behavior: A cell either primarily proliferates or primarily migrates. We analytically investigate an extreme form of the {"}Go or Grow{"} hypothesis where tumor cell motility and cell proliferation are considered as separate processes. Different so- lution types are examined via approximate solution of traveling wave equations, and we determine conditions for various wave front forms.",
keywords = "Glioblastoma, Go or grow, Mathematical modeling, Traveling wave, Tumor growth",
author = "Stepien, {Tracy L.} and Rutter, {Erica M.} and Yang Kuang",
note = "Funding Information: ∗Received by the editors September 5, 2017; accepted for publication (in revised form) March 12, 2018; published electronically June 20, 2018. http://www.siam.org/journals/siap/78-3/M114625.html Funding: The third author{\textquoteright}s work was partially supported by NSF grants DMS-1518529 and DMS-1615879. †School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287. Current address: Department of Mathematics, University of Arizona, Tucson, AZ 85719 (stepien@math.arizona.edu). ‡School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287. Current address: Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (erutter@ncsu.edu). §School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 (kuang@asu.edu). Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",
year = "2018",
doi = "10.1137/17M1146257",
language = "English (US)",
volume = "78",
pages = "1778--1801",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}