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

Abstract

AbstractWe study the large time behavior of non‐negative solutions to the nonlinear fractional reaction–diffusion equation ∂tu = − tσ( − Δ)α ∕ 2u − h(t)up (α ∈ (0,2]) posed on and supplemented with an integrable initial condition, where σ ≥ 0, p > 1, and h : [0, ∞ ) → [0, ∞ ). Defining the mass , 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 , then there exists M ∞ ∈ (0, ∞ ) such that ; if , then . Copyright © 2014 John Wiley & Sons, Ltd.