Kinetics of crystal growth in non-isochemical systems is considered taking into account the changes in composition of the residual melt during the process. This leads to the formation of concentration gradients in the vicinity of the new phase. If a component acting as a network modifier is enriched in the crystalline phase, the melt at the interface is enriched in network formers and the glass network will turn from floppy to rigid. Consequently, the crystal grows until a critical concentration is reached, at which the melt locally turns to a rigid one. There is a critical size of the crystal, above which the growth rate strongly decreases because the network former concentration at the interface drops below the threshold limit. The problem is solved numerically and finite differences are used for space and time discretization.

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A revised version of the concavity method of Levine, based on a new ordinary differential inequality, is proposed. Necessary and sufficient condition for nonexistence of global solutions of the inequality is proved. As an application, finite time blow up of the solution to Klein-Gordon equation with arbitrary positive initial energy is obtained under very general structural conditions.