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

Publicated to:Mathematics In Engineering. 4 (3): - 2022-01-01 4(3), DOI: 10.3934/mine.2022022

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

Affiliations

Consejo Nacl Invest Cient & Tecn, UBA, IMAS, Pab 1, RA-1428 Buenos Aires, DF, Argentina - Author
CSIC, UAM, UCM, Inst Ciencias Matemat ICMAT,UC3M, Madrid 28049, Spain - 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
Univ Autonoma Madrid, Dept Matemat, Madrid 28049, Spain - Author
Universidad Autónoma de Madrid - Author
Universidad de Buenos Aires - Author
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Abstract

We study the decay/growth rates in all Lp norms of solutions to an inhomogeneous nonlocal heat equation in RN involving a Caputo α-time derivative and a power β of the Laplacian when the dimension is large, N > 4β. Rates depend strongly on the space-time scale and on the time behavior of the spatial L1 norm of the forcing term.

Keywords

Caputo derivativeFractional laplacianFully nonlocal heat equationsHeat equation with nonlocal time derivativeLarge-time behavior

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematics In Engineering 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, 2022, it was in position , thus managing to position itself as a Q2 (Segundo Cuartil), in the category Analysis. Notably, the journal is positioned en el Cuartil Q4 for the agency WoS (JCR) in the category Mathematics, Interdisciplinary Applications.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 1.43, which 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: 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:

  • Scopus: 1

Impact and social visibility

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Additionally, the work has been submitted to a journal classified as Diamond in relation to this type of editorial policy.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://repositorio.uam.es/handle/10486/704491

Leadership analysis of institutional authors

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

the author responsible for correspondence tasks has been QUIROS GRACIAN, FERNANDO.