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R. I. and A. S. are partially supported by the Spanish project PID2020-115273GB-I00. A. I. M. is partially supported by the Spanish project RTI2018-098743-B-100.

Analysis of institutional authors

Iagar, RgCorresponding AuthorMunoz, AiAuthorSanchez, AAuthor

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September 27, 2022
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SELF-SIMILAR BLOW-UP PATTERNS FOR A REACTION-DIFFUSION EQUATION WITH WEIGHTED REACTION IN GENERAL DIMENSION

Publicated to:Communications On Pure And Applied Analysis. 21 (3): 891-925 - 2022-03-01 21(3), DOI: 10.3934/cpaa.2022003

Authors: Gabriel Iagar, Razvan; Isabel Munoz, Ana; Sanchez, Ariel

Affiliations

Univ Rey Juan Carlos, Dept Matemat Aplicada Ciencia & Ingn Mat & Tecnol, Madrid 28933, Spain - Author

Abstract

We classify the finite time blow-up profiles for the following reaction-diffusion equation with unbounded weight: partial derivative(t)u = Delta u(m) + vertical bar x vertical bar(sigma) u(p), posed in any space dimension x is an element of R-N, t >= 0 and with exponents m > 1, p is an element of (0,1) and sigma > 2(1-p)/(m-1). We prove that blow-up profiles in backward self-similar form exist for the indicated range of parameters, showing thus that the unbounded weight has a strong influence on the dynamics of the equation, merging with the nonlinear reaction in order to produce finite time blow-up. We also prove that all the blow-up profiles are compactly supported and might present two different types of interface behavior and three different possible good behaviors near the origin, with direct influence on the blow-up behavior of the solutions. We classify all these profiles with respect to these different local behaviors depending on the magnitude of sigma. This paper generalizes in dimension N > 1 previous results by the authors in dimension N = 1 and also includes some finer classification of the profiles for sigma large that is new even in dimension N = 1.

Keywords

BehaviorBlow-upClassificationExistenceGlobal-solutionsLocalized reactionNonexistencePhase space analysisPorous-medium equationReaction-diffusion equationsSelf-similar solutionsStrong reactionWeighted reactionZero points

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Communications On Pure And Applied Analysis 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 Q1 (Primer Cuartil), in the category Analysis.

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: 2.63. 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: 1.74 (source consulted: FECYT Feb 2024)
  • Field Citation Ratio (FCR) from Dimensions: 5.41 (source consulted: Dimensions Aug 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-08-29, the following number of citations:

  • WoS: 7
  • Scopus: 8

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.

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Iagar, Razvan Gabriel) and Last Author (Sánchez Valdés, Ariel).

the author responsible for correspondence tasks has been Iagar, Razvan Gabriel.