Decay of mass for a semilinear heat equation with mixed local-nonlocal operators

In this paper, we are concerned with the Cauchy problem for the reaction-diffusion equation ∂tu+tβLu=-h(t)up posed on RN, driven by the mixed local-nonlocal operator L=-Δ+(-Δ)α/2, α∈(0,2), and supplemented with a nonnegative integrable initial data, where p>1, β≥0, and h:(0,∞)→(0,∞) is a locally integrable function. We study the large time behavior of non-negative solutions and show that the nonlinear term determines the large time asymptotic for p≤1+α/N(β+1), while the classical/anomalous diffusion effects win if p>1+α/N(β+1).