@article{a4e9a7a27d254e3ea08cda251a6fe214,
title = "Convex compact sets in RN−1 give traveling fronts of cooperation–diffusion systems in RN",
abstract = "This paper studies traveling fronts to cooperation–diffusion systems in RN for N≥3. We consider (N−2)-dimensional smooth surfaces as boundaries of strictly convex compact sets in RN−1, and define an equivalence relation between them. We prove that there exists a traveling front associated with a given surface and show its stability. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.",
keywords = "Cooperation–diffusion system, Non-symmetric, Traveling front",
author = "Masaharu Taniguchi",
note = "Funding Information: The author would like to express his sincere gratitude to Professor Wei-Ming Ni of East China Normal University and University of Minnesota and Professor Hirokazu Ninomiya of Meiji University for valuable comments and suggestions. Special thanks go to Prof. Zhi-Cheng Wang of Lanzhou University for valuable discussions. This work is supported by JSPS Grant-in-Aid for Scientific Research (C) Grant Number 26400169 . Finally the author thanks the referee who carefully checked this paper and gave valuable comments and suggestions. Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",
year = "2016",
month = mar,
day = "5",
doi = "10.1016/j.jde.2015.11.010",
language = "English",
volume = "260",
pages = "4301--4338",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "5",
}