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Some special solutions of self similar type in MHD, obtained by a separation method of variables

Michel Cessenat, Philippe Genta (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables Φ1, Φ2, Φ3 in addition to the time variable t and then in searching a solution which is separated with respect to Φ1 and t only. This is allowed by a very simple relation, called a “metric separation equation”, which governs the type of solutions with respect to time. The families...

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