Decay of mass for nonlinear equation with fractional Laplacian

The large time behavior of non-negative solutions to the reaction–diffusion equation ?_t u=-(-D)^a/2u - u^p{partial_t u=-(-Delta)^{alpha/2}u - u^p}, ${(alphain(0,2], ;p > 1)}${(alphain(0,2], ;p > 1)} posed on mathbbR^N{mathbb{R}^N} and supplemented with an integrable initial condition is studied. We show that the anomalous diffusion term determines the large time asymptotics for p > 1 + α/N, while nonlinear effects win if p ≤ 1 + α/N.