Fisher-KPP equation with Robin boundary conditions on the real half line

We consider the Fisher-KPP equation with Robin boundary conditions on the half line. We show that this problem has even number of nonnegative stationary solutions, which are ordered, a stable one is sandwiched by two unstable ones. Then we construct several types of entire solutions between them, each entire solution connects an unstable stationary solution with a stable one. In particular, we construct two types of entire solutions U-c(x, t) and U(x, t) connecting 0 and the smallest positive stationary solution. In addition, U-c tend to the traveling wave solution with speed c as t -> -infinity in a moving frame, and U(x, t) enjoys convexity. This paper extends the recent results of Lou, Lu and Morita in Lou et al. (2020) from Dirichlet boundary condition to Robin boundary condition. (c) 2022 Elsevier Ltd. All rights reserved.