Decay of mass for fractional evolution equation with memory term

Abstract

We investigate the decay properties of the mass M ( t ) = ∫ R N u ( ⋅ , t ) d x M(t)= \int _{\mathbb {R}^N} u(\cdot ,t)dx of the solutions of a fractional diffusion equation with nonlinear memory term. We show, using a suitable class of initial data and a restriction on the diffusion and nonlinear term, that the memory term determines the large time asymptotics; that is, M ( t ) M(t) tends to zero as t → ∞ . t\to \infty .