@article{8e3f1495bd1a4ec8931c3b5066d55e56,
title = "Representation formulas of solutions and bifurcation sheets to a nonlocal allen-cahn equation",
abstract = "We are interested in the Neumann problem of a 1D stationary Allen-Cahn equation with a nonlocal term. In our previous papers [4] and [5], we obtained a global bifurcation branch, and showed the existence and uniqueness of secondary bifurcation point. At this point, asymmetric solutions bifurcate from a branch of odd-symmetric solutions. In this paper, we give representation formulas of all solutions on the secondary bifurcation branch, and a bifurcation sheet which consists of bifurcation curves with heights.",
keywords = "Allen-Cahn equation, Exact solution, Nonlocal term",
author = "Tatsuki Mori and Kousuke Kuto and Tohru Tsujikawa and Shoji Yotsutani",
note = "Funding Information: K. Kuto was supported by Grant-in-Aid. for Scientific Research (C) 19K03581. T. Tsujikawa was supported by Grant-in-Aid. for Scientific Research (C) 17K05334. S. Yotsutani was supported by Grant-in-Aid. for Scientific Research (C) 19K03593. This work was supported by Joint Research Center for Science and Technology of Ryukoku University in 2020. ∗ Corresponding author: Shoji Yotsutani. Publisher Copyright: {\textcopyright} 2020 American Institute of Mathematical Sciences. All rights reserved.",
year = "2020",
month = aug,
doi = "10.3934/dcds.2020205",
language = "English",
volume = "40",
pages = "4907--4925",
journal = "Discrete and Continuous Dynamical Systems- Series A",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "8",
}