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Iagar, RgCorresponding AuthorLatorre, MAuthorSanchez, AAuthor

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BLOW-UP PATTERNS FOR A REACTION-DIFFUSION EQUATION WITH WEIGHTED REACTION IN GENERAL DIMENSION

Publicated to:Advances In Differential Equations. 29 (7-8): 515-574 - 2024-08-01 29(7-8), DOI: 10.57262/ade029-0708-515

Authors: Iagar, Razvan Gabriel; Latorre, Marta; Sanchez, Ariel

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Abstract

We classify all the blow-up solutions in self -similar form to the following reaction-diffusion equation partial derivative(t)u= triangle u(m)+|x|(sigma)u(p), posed for (x, t) is an element of R(N )x (0,T), with m >1, 1 <= p < m and -2(p-1)/(m-1) < sigma < infinity. We prove that there are several types of self -similar solutions with respect to the local behavior near the origin, and their existence depends on the magnitude of sigma. In particular, these solutions have different blow-up sets and rates: some of them have x = 0 as a blow-up point, some other only blow up at (space) infinity. We thus emphasize on the effect of the weight on the specific form of the blow-up patterns of the equation. The present study generalizes previous works by the authors limited to dimension N = 1 and sigma > 0.

Keywords

ClassificationExistenceGlobal-solutionsHeat-equationsNonexistenceParabolic equationsSolvabilitySpace infinityWell-posednessZero points

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Advances In Differential Equations due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 98/332, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-06-06:

  • WoS: 4
  • Scopus: 4

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.