## References

Antontsev, S.N. and de Oliveira, H.B.. 2008. Qualitative properties of the ice-thickness in a 3D model. WSEAS Trans. Math., 7(3), 78–86.

Bodvarsson, G.
1955. On the flow of ice-sheets and glaciers. Jökull, 5, 1–8.

Brezis, H.
1999. Analyse fonctionnelle: théorie et applications. Paris, Éditions Dunod.

Brock, F.
2000. Continuous rearrangement and symmetry of solutions of elliptical problems. Proc. Indian Acad. Sci. (Math. Sci.), 110(2), 157–204.

Bueler, E.
2003. Construction of steady state solutions for isothermal shallow ice sheets. Fairbanks, AK, University of Alaska Fairbanks. Department of Mathematics and Statistics. (UAF DMS Tech. Rep. 03-02.)

Bueler, E., Lingle, C.S., Kallen-Brown, J.A., Covey, D. N. and Bowman, L. N.. 2005. Exact solutions and verification of numerical models for isothermal ice sheets. J. Glaciol., 51(173), 291–306.

Bueler, E., Brown, J. and Lingle, C.. 2007. Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification. J. Glaciol., 53(182), 499–516.

Calvo, N., Díaz, J.I., Durany, J., Schiavi, E. and Vázquez, C.. 2002. On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics. SIAM J. Appl. Math., 63(2), 683–707.

Dacorogna, B.
2008. Direct methods in the calculus of variations. Second edition. New York, Springer.

Evans, L.C.
1999. Partial differential equations. Providence, RI, American Mathematical Society.

Glen, J.W.
1958. The flow law of ice: a discussion of the assumptions made in glacier theory, their experimental foundation and consequences. IASH Publ.
47 (Symposium at Chamonix 1958 – *Physics of the Movement of the Ice*), 171–183.

Greve, R. and Blatter, H.. 2009. Dynamics of ice sheets and glaciers. Dordrecht, etc., Springer.

Gudmundsson, G.H.
1997. Basal-flow characteristics of a nonlinear flow sliding frictionless over strongly undulating bedrock. J. Glaciol., 43(143), 80–89.

Halfar, P.
1981. On the dynamics of the ice sheets. J. Geophys. Res., 86(C11), 11,065–11,072.

Halfar, P.
1983. On the dynamics of the ice sheets 2. J. Geophys. Res., 88(C10), 6043–6051.

Huybrechts, P., Payne, T. and the EISMINT Intercomparison Group. 1996. The EISMINT benchmarks for testing ice-sheet models. Ann. Glaciol., 23, 1–12.

Lieb, E.H. and Loss, M.. 1997. Analysis. Providence, RI, American Mathematical Society.

Lü, H., O’Regan, D. and Agarwal, R.P.. 2005. Positive solutions for singular *p*-Laplacian equations with sign changing nonlinearities using inequality theory. Appl. Math. Comput., 165(3), 587–597.

Oerlemans, J.
1981. Some basic experiments with a vertically-integrated ice sheet model. Tellus, 33(1), 1–11.

Paterson, W.S.B.
1994. The physics of glaciers. Third edition. Oxford, etc., Elsevier.

Picasso, M., Rappaz, J., Reist, A., Funk, M. and Blatter, H.. 2004. Numerical simulation of the motion of a two-dimensional glacier. Int. J. Num. Meth. Eng., 60(5), 995–1009.

Raviart, P.A.
1970. Sur la résolution de certaines équations paraboliques non linéaires. J. Funct. Anal., 5(2), 299–328.

Van den Berg, J., van de Wal, R.S.W. and Oerlemans, J.. 2006. Effects of spatial discretization in ice-sheet modelling using the shallow-ice approximation. J. Glaciol., 52(176), 89–98.

Van der Veen, C.J.
1999. Fundamentals of glacier dynamics. Rotterdam, A.A. Balkema.

Vialov, S.S.
1958. Regularities of glacial shields movement and the theory of plastic viscous flow. IASH Publ.
47 (Symposium at Chamonix, 1958 – *Physics of the Movement of the Ice*), 266–275.

Weertman, J.
1957. On the sliding of glaciers. J. Glaciol., 3(21), 33–38.

Weertman, J.
1961. Stability of ice-age ice sheets. J. Geophys. Res., 66(11), 3783–3792.

Weertman, J.
1964. The theory of glacier sliding. J. Glaciol., 5(39), 287–303.