Abstract
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:
if p > 1 + alpha/N(sigma+1),then lim (t ->infinity) M(t) =0.then there exists M
if p > 1 + alpha/N(sigma+1),then lim (t ->infinity) M(t) =0. Copyright (c) 2014 John Wiley & Sons, Ltd.