The Decay of mass for a nonlinear fractional reaction-diffusion equation

摘要

We study the large time behavior of non-negative solutions to the nonlinear fractional reaction-diffusion equation (t)u=-t(sigma)(-)(/2)u-h(t)u(p) ((0,2]) posed on RN and supplemented with an integrable initial condition, where sigma 0, p>1, and h : [0,)[0,). Defining the mass M(t) =RNu(x,t)dx, under certain conditions on the function h, we show that the asymptotic behavior of the mass can be classified along two cases as follows: