A family of nonlinear diffusion equations related to the q-error function

A.R. Plastino, C. Tsallis and R.S. Wedemann

Physica A: Statistical Mechanics and its Applications, 2024, vol. 635, issue C

Abstract: We investigate a bi-parametric family of nonlinear diffusion equations that includes, as special members, the power-law nonlinear diffusion equation, and an evolution equation akin to Ubriaco’s nonlinear diffusion equation. It is well-known that the power-law nonlinear diffusion equation is closely related to the Sq-thermostatistics. We show that the Ubriaco-like member of the above mentioned bi-parametric family is also related to the Sq-theory, because it admits exact time-dependent solutions that exhibit the q-error-function shape. These solutions constitute a generalization, within the Sq-thermostatistical framework, of a celebrated class of solutions of the linear diffusion equation, that have the standard error-function form. Besides exploring the main aspects of a family of non-standard diffusion processes, our present developments constitute a physical-mathematical application of the q-error-function. This function, in spite of its potential relevance for q-statistics and its applications, has not yet attracted the attention it deserves from the Sq-thermostatistics research community.

Keywords: Nonlinear diffusion; q-error function; Sq-thermostatistics; Ubriaco diffusion equation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:635:y:2024:i:c:s0378437123010300

DOI: 10.1016/j.physa.2023.129475

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