2010/12/31 by Alexander N. Gorban, A. N. Gorban, H. P. Sargsyan +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Fractional Differential Equations Solutions #Numerical methods in inverse problems #cond-mat.mtrl-sci #physics.chem-ph
paper · pdf · doi:10.1051/mmnp/20116509
published as Mathematical Modelling of Natural Phenomena, Volume 6 / Issue 05, (2011), 184-262. Mathematical Modelling of Natural Phenomena, Volume 6 / Issue 05, (2011), 184-262 · 81 pages, Bibliography 118 references, a review paper (v4: the final published version)
openalex publication_date 2011/01/01 · arxiv created 2012/05/01 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of the reaction mechanism borrowed from chemical kinetics.