Fisher–KPP equation with Robin boundary conditions on the real half line. (September 2022) - Suo, Jinzhe; Tan, Kaiyuan
Abstract: 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 → − ∞ 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.