Convection-Diffusion-Reaction equation with similarity solutions
arXiv:1805.12531 · doi:10.1016/j.cjph.2019.02.030
Abstract
We consider similarity solutions of the generalized convection-diffusion-reaction equation with both space- and time-dependent convection, diffusion and reaction terms. By introducing the similarity variable, the reaction-diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable convection-diffusion-reaction systems. Some representative examples of exactly solvable systems are presented. We also describe how an equivalent convection-diffusion-reaction system can be constructed which admits the same similarity solution of another convection-diffusion-reaction system.
arXiv comment9 pages, 6 figures. arXiv admin note: text overlap with arXiv:1508.00167
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