Environmental contaminant dispersion models based on the Vladimirov-Taibleson p-adic pseudo-differential operator
Year: 2025
Type: article
Abstract: This research develops a new framework for modeling the dispersion of contaminants in non-Archimedean media using the Taibleson-Vladimirov $$D^{\alpha }$$ D α p -adic pseudo-differential operator. A p -adic differential equation is proposed and solved, modeling the dispersion of contaminants in a p -adic medium initially confined to a specific region. Additionally, it is analyzed how the p -adic heat kernel associated with the Taibleson-Vladimirov $$D^{\alpha }$$ D α operator serves as a powerful tool for understanding how contaminants disperse over time, making the heat kernel a cornerstone for mathematical models aimed at environmental applications in p -adic settings. Furthermore, through the heat equation associated with the Taibleson-Vladimirov $$D^{\alpha }$$ D α operator, the evolution of contaminant concentration over time is described. Finally, a stochastic fractional p -adic diffusion equation is formulated and solved, incorporating initial conditions, external sources, and random noise.
Institutions: University of Sucre, University of Atlántico
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4412363054