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

We study the large time behavior of non‐negative solutions to the nonlinear fractional reaction–diffusion equation ?_tu = ? t^σ( ? Δ)^{α ∕ 2}u ? h(t)u^p (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 .

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