Mathematical Models of Ice Shelves

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Abstract
For flat external ice shelves, expanding freely in all directions, the problem of thermodynamics is one-dimensional. In the affine dimensionless system of coordinates, equations of the dynamics together with the rheological equation lead to the non-linear integro-differential equation involving the reduced temperature. In the quasi-steady case the boundary problem for this equation is solved by means of the method of combining asymptotic expansions. It is shown that if ice is coming from the upper and lower surfaces in the opposite directions the regime is unsteady because of the internal heat accumulation. The integro-differential equation for the temperature in the case of thinning internal ice shelves is more complicated, but it can be solved by a method analogous to the one mentioned above.

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