info:eu-repo/semantics/article
Large-time behavior for a fully nonlocal heat equation
Fecha
2021-09Registro en:
Cortázar, Carmen; Quirós, Fernando; Wolanski, Noemi Irene; Large-time behavior for a fully nonlocal heat equation; Springer; Vietnam Journal of Mathematics; 49; 3; 9-2021; 831-844
2305-221X
2305-2228
CONICET Digital
CONICET
Autor
Cortázar, Carmen
Quirós, Fernando
Wolanski, Noemi Irene
Resumen
We study the large-time behavior in all Lp norms and in different space-time scales of solutions to a nonlocal heat equation in ℝN involving a Caputo α-time derivative and a power of the Laplacian (−Δ)s, s ∈ (0,1), extending recent results by the authors for the case s = 1. The initial data are assumed to be integrable, and, when required, to be also in Lp. The main novelty with respect to the case s = 1 comes from the behaviour in fast scales, for which, thanks to the fat tails of the fundamental solution of the equation, we are able to give results that are not available neither for the case s = 1 nor, to our knowledge, for the standard heat equation, s = 1, α = 1.