Abstract
Previous analytical simplifications of Boltzmann's similarity solution are unified and generalized by examining symmetry and transformation properties of the equation. It is shown how to reduce boundary value problems to initial value problems for certain diffusivities. A series solution is derived for this case, and shown to be accurate for a broad range of parameter values.
Résumé
Les simplifications analytiques connues de la solution similaire de Boltzmann sont unifiées et généralisées par l'étude des propriétés de symétrie et des transformations de l'équation de diffusion. On montre comment, pour certaines diffusivités, un problème de conditions aux limites se réduit à un problème de valeurs initiales. Une solution en séries obtenue pour ce cas est très précise pour un domaine étendu des paramètres.
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Lisle, I.G., Parlange, J.Y. Analytical reduction for a concentration dependent diffusion problem. Z. angew. Math. Phys. 44, 85–102 (1993). https://doi.org/10.1007/BF00914355
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DOI: https://doi.org/10.1007/BF00914355