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 Uc(x,t) and U(x,t) connecting 0 and the smallest positive stationary solution. In addition, Uc 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.
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