Fernando Quirós

We study the large-time behaviour of solutions to inhomogeneous heat equations in the whole space, with a diffusion operator which may be local or nonlocal both in space and time. We find that the asymptotic profiles depend strongly on the space-time scale and on the time behaviour of the spatial $L^1$ norm of the forcing term. Some of our results are surprising even for the classical heat equation in the somewhat studied case in which the right-hand side is globally integrable in space and time. On the other hand, our assumptions on the source term allow for the space integral to grow to infinity as time goes to infinity. This is joint work with Noemí Wolanski (IMAS-UBA-CONICET, Argentina) and Carmen Cortázar (PUC, Chile), done mostly within the framework of GHAIA.