Asymptotic profiles for inhomogeneous heat equations with memory

We study the large-time behavior 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 dimension is large, N > 4 β . The asymptotic profiles depend strongly on the space-time scale and on the t...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische annalen 2024-08, Vol.389 (4), p.3705-3746
Main Authors: Cortázar, Carmen, Quirós, Fernando, Wolanski, Noemí
Format: Article
Language:English
Subjects:
Asymptotic properties
Mathematics
Mathematics and Statistics
Thermodynamics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the large-time behavior 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 dimension is large, N > 4 β . The asymptotic profiles depend strongly on the space-time scale and on the time behavior of the spatial L 1 norm of the forcing term.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-023-02707-6