Decay/growth rates for inhomogeneous heat equations with memory. The case of small dimensions

2022/04/24 by Carmen Cortázar, Cortázar, Carmen, Fernando Quirós +3
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2204.11342

Abstract

We study the decay/growth rates in all L^p norms of solutions to an inhomogeneous nonlocal heat equation in ℝ^N involving a Caputo α-time derivative and a power β of the Laplacian when the spatial dimension is small, 1≤ N≤ 4β, thus completing the already available results for large spatial dimensions. Rates depend not only on p, but also on the space-time scale and on the time behavior of the spatial L¹ norm of the forcing term.

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