Large-Time Behavior for a Fully Nonlocal Heat Equation

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Large-Time Behavior for a Fully Nonlocal Heat Equation

Publicated to:Vietnam Journal of Mathematics. (3): 831-844 - 2021-09-01 (3), DOI: 10.1007/s10013-020-00452-w

Authors: Cortazar, Carmen; Quiros, Fernando; Wolanski, Noemi

Affiliations

Consejo Nacional de Investigaciones Científicas y Técnicas - Author

CSIC-UAM-UC3M-UCM - Instituto de Ciencias Matematicas (ICMAT) - Author

Pontificia Univ Catolica Chile, Dept Matemat, Santiago, Chile - Author

Pontificia Universidad Católica de Chile - Author

UBA, IMAS, CONICET, Ciudad Univ,Pabellon 1, RA-1428 Buenos Aires, DF, Argentina - Author

UC3M, UCM, UAM, Inst Ciencias Matemat ICMAT,CSIC, Madrid 28049, Spain - Author

Univ Autonoma Madrid, Dept Matemat, Madrid 28049, Spain - Author

Universidad Autónoma de Madrid - Author

Abstract

© 2020, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 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.

Keywords

asymptotic behaviorcaputo derivativefractional laplacianAsymptotic behaviorCaputo derivativeFractional diffusionFractional laplacianFully nonlocal heat equation

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Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Vietnam Journal of Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2021, it was in position , thus managing to position itself as a Q2 (Segundo Cuartil), in the category Mathematics (Miscellaneous).

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.66. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

Weighted Average of Normalized Impact by the Scopus agency: 1.67 (source consulted: FECYT Feb 2024)
Field Citation Ratio (FCR) from Dimensions: 3.21 (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-27, the following number of citations:

WoS: 4
Scopus: 6

Impact and social visibility

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Argentina; Chile.

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