TY - JOUR
T1 - Threshold Solutions for Nonlocal Reaction Diffusion Equations
AU - Zhang , He
AU - Li , Yong
AU - Yang , Xue
JO - Communications in Mathematical Research 
VL - 3
SP - 389
EP - 421
PY - 2022
DA - 2022/08
SN - 38
DO - http://doi.org/10.4208/cmr.2022-0003
UR - https://global-sci.org/intro/article_detail/cmr/20962.html
KW - Nonlocal reaction diffusion equation, asymptotic behaviors, threshold solution, sharp transition.
AB - <p style="text-align: justify;">We study the Cauchy problem for nonlocal reaction diffusion equations with bistable nonlinearity in 1D spatial domain and investigate the asymptotic behaviors of solutions with a one-parameter family of monotonically increasing and compactly supported initial data. We show that for small values
of the parameter the corresponding solutions decay to 0, while for large values the related solutions converge to 1 uniformly on compacts. Moreover, we
prove that the transition from extinction (converging to 0) to propagation (converging to 1) is sharp. Numerical results are provided to verify the theoretical
results.</p>