Asymptotic behavior of solutions of a degenerate Fisher–KPP equation with free boundaries

The aim of this paper is to study the asymptotic behavior of solutions of a degenerate Fisher–KPP equation ut=uxx+up(1−u)(p>0) in the domain {(t,x)∈R2:t≥0,x∈[g(t),h(t)]}{(t,x)∈R2:t≥0,x∈[g(t),h(t)]}, where g(t)g(t) and h(t)h(t) are two free boundaries. For p>1p>1 we obtain trichotomy result: spreading ([g(t),h(t)]→R[g(t),h(t)]→R and u(t,⋅)→1u(t,⋅)→1 locally uniformly in RR), vanishing (h(t)−g(t)<∞h(t)−g(t)<∞ and u(t,⋅)→0u(t,⋅)→0 uniformly in [g(t),h(t)][g(t),h(t)]), and virtual vanishing   ([g(t),h(t)]→R[g(t),h(t)]→R and u(t,⋅)→0u(t,⋅)→0 uniformly in [g(t),h(t)][g(t),h(t)]). For 0