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Solitary waves in magma dynamics. (English) Zbl 0674.76093
Summary: We investigate the stability of the one-dimensional solitary waves solutions of the equations proposed by D. P. McKenzie [The generation and compaction of partially molten rock, J. Petrol. 25, 713- 765 (1984)] to model the ascent of melts in the Earth interior. We show that for small porosity and two-dimensional horizontal disturbances with long wavelength, these solitary waves are unstable. We also exhibit two- and three-dimensional solitary-wave solutions of the McKenzie equations.

MSC:
76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics
86A99 Geophysics
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