Díaz Díaz, Jesús IldefonsoFowler, A.C.Muñoz, A.I.Schiavi, E.2023-06-202023-06-202009DÍAZ, J. I., FOWLER, A. C., MUÑOZ, A. I., SCHIAVI, 2008, Mathematical analysis of a Model of River Channel Formation. Pure and Applied Geophysics, Birkhäuser Verlag, Basel,165. DOI: 10.1007/s00024-004-0394-3 EVANS, L. C., GARIEPY, R. F., Measure Theory and Fine Properties of Functions, (Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992) FOWLER, A. C., KOPTEVA, N., OAKLEY, C., (2007), The formation of river channels. SIAM J. Appl. Maths, 67, 1016–1040. LOEWENHERZ-LAWRENCE, D. S., (1994), Hydrodynamic description for advective sediment transport processes and rill initiation, Water Resour. Res. 30, 3203–3212. LOEWENHERZ-LAWRENCE, D. S., (1994), Hydrodynamic description for advective sediment transport processes and rill initiation. Water Resour. Res. 30, 3203–3212. MEYER-PETER, E., MULLER, R., (1948), Formulas for bed-load transport. Proc. Int. Assoc. Hydraul. Res., 3rd annual conference, Stockholm, 39–64. SAMARSKI, A. A., GALAKTIONOV, V. A., KURDYUMOV, S. P., MIKHAILOV, A. P., Blow-up in quasilinear. parabolic equations. (Walter de Gruyter, Berlin, 1995). SMITH, T. R., BRETHERTON, F. P., (1972), Stability and the conservation of mass in drainage basin evolution. Water Resour. Res., 8, 11, 1506–1529.https://hdl.handle.net/20.500.14352/51366A coupled model describing the evolution of the topographic elevation and the depth of the overland water film is here studied when considering the overland flow of water over an erodible sediment. We complete the previous modelling of the problems by SMITH and BRETHERTON (1972) and FOWLER et al. (2007), obtaining a model which involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. The degeneracy of the equation causes the channel width to be self-selecting. We propose here a global formulation of the problem, formulated in the whole space, beyond the support of the solution. An important feature of the model proposed here is that despite of the presence of the superlinear forcing term at the equation, a solution to it can not blow up thanks to the mass constraint.engjournal articlehttp://www.unizar.es/acz/05Publicaciones/Monografias/MonografiasPublicadas/Monografia31/057.pdfhttp://www.unizar.es/open access51River ModelsLandscape EvolutionNonlinear parabolic equationsFree boundariessingular free boundary flux.Matemáticas (Matemáticas)12 Matemáticas