Abstract
Motivated by geophysical applications we develop a number of mathematical models of the time-dependent crystallization in magma chambers, lava lakes and similar systems which involve nonlinear mechanisms of the melt convection and interfacial kinetics. The Stefan-type moving boundary models including important nonlinear physical dependences are solved analytically for different solidification stages. An influence of the convection intensity and undercooling degree on nonlinear solidification dynamics is discussed.
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