Anomalous diffusion with absorption: Exact time-dependent solutions

TL;DR

This paper extends exact solutions of a nonlinear Fokker-Planck equation for anomalous diffusion to include homogeneous absorption, revealing complex interactions between force, diffusion, and absorption.

Contribution

It introduces new analytical solutions for anomalous diffusion with absorption, expanding previous models to account for homogeneous absorption effects.

Findings

Exact time-dependent solutions derived

Absorption influences diffusion behavior significantly

Interplay between force, diffusion, and absorption analyzed

Abstract

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion and the absorption process are discussed.