Asymptotic profiles for inhomogeneous heat equations with memory

Abstract

AbstractWe study the large-time behavior in all $$L^p$$ L p norms of solutions to an inhomogeneous nonlocal heat equation in $${\mathbb {R}}^N$$ R N involving a Caputo $$\alpha $$ α -time derivative and a power $$\beta $$ β of the Laplacian when the dimension is large, $$N> 4\beta $$ N > 4 β . The asymptotic profiles depend strongly on the space-time scale and on the time behavior of the spatial $$L^1$$ L 1 norm of the forcing term.