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

Mathematics in Engineering

Carmen Cortázar¹  Fernando Quirós²  Noemí Wolanski³ 

[1] 1. Departamento de Matemática, Pontificia Universidad Católica de Chile, Santiago, Chile;2. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049-Madrid, Spain 3. Instituto de Ciencias Matemáticas ICMAT (CSIC-UAM-UCM-UC3M), 28049-Madrid, Spain;4. IMAS-UBA-CONICET, Ciudad Universitaria, Pab. I, (1428) Buenos Aires, Argentina;

关键词: heat equation with nonlocal time derivative;    caputo derivative;    fully nonlocal heat equations;    fractional laplacian;    large-time behavior;   

DOI  :  10.3934/mine.2022022

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown