Journal
MATHEMATICS IN ENGINEERING
Volume 4, Issue 3, Pages -Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mine.2022022
Keywords
heat equation with nonlocal time derivative; Caputo derivative; fully nonlocal heat equations; fractional Laplacian; large-time behavior
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Funding
- European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant [777822]
- FONDECYT (Chile) [1190102]
- Ministerio de Econom'ia y Competitividad (Spain) [MTM2017-87596-P]
- Ministerio de Ciencia e Innovacion (Spain) [CEX2019-000904-S]
- CONICET [PIP 11220150100032CO]
- ANPCyT [PICT2016-1022]
- UBACYT [20020150100154BA]
- MathAmSud (Argentina) [13MATH03]
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This study focuses on the decay/growth rates in all L-p norms of solutions to an inhomogeneous nonlocal heat equation in a large dimension space, N > 4 beta. The rates are strongly influenced by the space-time scale and the time behavior of the spatial L-1 norm of the forcing term.
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 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.
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