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Existence and stability of steady-state solutions of the shallow-ice-sheet equation by an energy-minimization approach

  • Guillaume Jouvet (a1), Jacques Rappaz (a1), Ed Bueler (a2) and Heinz Blatter (a3)

Abstract

The existence of solutions of the non-sliding shallow-ice-sheet equation on a flat horizontal bed with a mass balance linearly depending on altitude is proven for fixed margins. Free-margin solutions for the same mass balance do not exist. Fixed-margin solutions show unbounded shear stress and nonzero mass flux at the margin. Steady-state solutions with realistic margins, vanishing ice flux and vanishing shear stress are found numerically for ice sheets with Weertman-type sliding.

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References

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