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We consider a generalized Richards equation with power-law nonlinearities modelingfiltration in porous media. Conditions are derived under which the problem can be reduced to thelinear heat equation or to nonlinear equations with known solutions. The families of explicit exactsolutions that can be expressed via elementary functions or Lambert’s \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$W$$\end{document}-function are found. Some examples illustrating theresults are given.
Differential Equations – Springer Journals
Published: Sep 8, 2020
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