Asymptotic behavior of generalized self-similar solutions for a nonlinear hybrid problem of porous medium equations

Mohamed Dilmi; Bilal Basti

doi:10.2478/aupcsm-2025-0007

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Asymptotic behavior of generalized self-similar solutions for a nonlinear hybrid problem of porous medium equations

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 25 (2025): Issue 1 (December 2025)

By: Mohamed Dilmi and Bilal Basti

Open Access

|Dec 2025

Abstract

The present paper investigates the asymptotic behavior of positive generalized self-similar solutions for a nonlinear hybrid problem involving n^th-order derivative porous medium equations. We provide sufficient conditions for the existence and uniqueness of weak solutions that have compact support and dynamic characteristics. Furthermore, we establish the behavior of these solutions by examining a specific set of variables and their signs, which must meet certain conditions to determine whether the solutions exist globally or locally in time.

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2025-0007 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 53 - 75

Submitted on: Feb 2, 2024

Accepted on: Sep 18, 2025

Published on: Dec 31, 2025

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

porous medium equation,

generalized self-similar solution,

blow-up,

Related subjects:

© 2025 Mohamed Dilmi, Bilal Basti, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 25 (2025): Issue 1 (December 2025)