Analytic solutions for irregular diffusion equations with concentration dependent diffusion coefficients
Statistical Mechanics
2023-11-09 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We investigate diffusion equations which have concentration dependent diffusion coefficients with physically two relevant Ans\"atze, the self-similar and the traveling wave Ansatz. We found that for power-law concentration dependence some of the results can be expressed with a general analytic implicit formulas for both trial functions. For the self-similar case some of the solutions can be given with a formula containing the hypergeometric function. For the traveling wave case different analytic formulas are given for different exponents. For some physically reasonable parameter sets the direct solutions are given and analyzed in details.
Cite
@article{arxiv.2310.01466,
title = {Analytic solutions for irregular diffusion equations with concentration dependent diffusion coefficients},
author = {I. F. Barna and L. Matyas},
journal= {arXiv preprint arXiv:2310.01466},
year = {2023}
}
Comments
13 pages 3 figures