Development of Interfaces in Nonlinear Multidimensional Reaction-Diffusion Equations With Parabolic p-Laplacian Properties

Roqia Abdullah Jeli

Journal of Applied Mathematics, 2025, vol. 2025, 1-13

Abstract: This research examines the behavior of interfaces in nonlinear multidimensional reaction–diffusion equations with parabolic p-Laplacian properties, which are applicable across a wide range of biological, physical, and chemical contexts. The value of this work lies in its contribution to understanding how interfaces behave under slow diffusion, shedding light on the complex interplay between diffusion and reaction forces. The study aims to analyze the existence and dynamics of interfaces governed by a Cauchy problem, particularly focusing on their expansion, contraction, or stability, influenced by different system parameters. The methodology incorporates the formulation of weak solutions, rescaling techniques, and self-similar solutions to derive detailed expressions for the local interface behavior. The main conclusion is that the behavior of the interface, whether it expands, contracts, or remains stable, is strongly governed by the parameters p, λ, and q. Additionally, the finite propagation speed ensures that the effects are confined, making the model applicable to practical scenarios such as tumor growth, porous media flow, and phase transitions.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jam/2025/4208036.pdf (application/pdf)
http://downloads.hindawi.com/journals/jam/2025/4208036.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:4208036

DOI: 10.1155/jama/4208036

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().