On Fisher's equation with the fractional p -Laplacian

In the present note, we show that if the initial date is between zero and one, then the global solution of a Dirichlet Fisher-KPP equation with the fractional (Figure presented.) -Laplacian is also between zero and one. As a consequence, a large-time behavior of the global solution is discussed. In addition, some blow-up results including a general Lipschitz nonlinearity are given. The proofs mainly rely on special symmetry and invariance properties of the fractional (Figure presented.) -Laplacian.